{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-08-24T00:15:41.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-08-24T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":61461,"title":"Calculate integrals using numerical methods 3.","description":"Now let's compare the 2 previous rules. Using the \"Simpson 1/3\" rule and the trapezoidal rule, NOT THE SIMPLE ONES, calculate the following integral:\r\n\r\nFurther explanations:\r\n1)the limits(a,b) will be given.\r\n2)The number of subspaces(n) of [a,b] will also be given.\r\n3)I1 is the integral of the Simpson rule. I2 the integral of the trapezoidal rule.\r\n4)ROUND THE RESULTS TO 4 DECIMAL PLACES!!!!!!!!!!!!\r\nGOOD LUCK!!!!!!!!!!!!!!!!!!!!!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 277px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 138.5px; transform-origin: 469px 138.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 21px; text-align: left; transform-origin: 445px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNow let's compare the 2 previous rules. Using the \"Simpson 1/3\" rule and the trapezoidal rule, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eNOT THE SIMPLE ONES\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, calculate the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv 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\" width=\"69\" height=\"46\" style=\"width: 69px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFurther explanations:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1)the limits(a,b) will be given.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2)The number of subspaces(n) of [a,b] will also be given.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3)I1 is the integral of the Simpson rule. I2 the integral of the trapezoidal rule.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4)ROUND THE RESULTS TO 4 DECIMAL PLACES!!!!!!!!!!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!!!!!!!!!!!!!!!!!!!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [I1 I2] = CompareS_T(a,b,n)\r\n    \r\nend ","test_suite":"%%\r\na = 1; \r\nb = 5; \r\nn = 2;\r\nI1_correct = round(2/3*log(405),4);\r\nI2_correct = round(log(45),4);\r\n[I1, I2] = CompareS_T(a,b,n);\r\nassert(abs(I1 - I1_correct) \u003c 1e-4 \u0026\u0026 abs(I2 - I2_correct) \u003c 1e-4)\r\n%%\r\na = 2; \r\nb = 8; \r\nn = 4;\r\nI1_correct = 9.2449;\r\nI2_correct = 9.1804;\r\n[I1, I2] = CompareS_T(a,b,n);\r\nassert(abs(I1 - I1_correct) \u003c 1e-4 \u0026\u0026 abs(I2 - I2_correct) \u003c 1e-6)\r\n%%\r\na = 5;\r\nb = 15;\r\nn = 8;\r\nI1_correct = 22.5734;\r\nI2_correct = 22.5563;\r\n[I1, I2] = CompareS_T(a,b,n);\r\nassert(abs(I1 - I1_correct) \u003c 1e-4 \u0026\u0026 abs(I2 - I2_correct) \u003c 1e-6)\r\n%%\r\ncode = fileread(which('CompareS_T'));\r\nhas_if = ~isempty(regexp(code, '\\bif\\b', 'once'));\r\nassert(~has_if, 'Using \"if\" is not allowed!')","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5158730,"edited_by":5158730,"edited_at":"2026-08-30T13:00:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2026-08-30T13:00:07.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-08-30T12:55:50.000Z","updated_at":"2026-08-31T15:31:58.000Z","published_at":"2026-08-30T13:00:07.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNow let's compare the 2 previous rules. Using the \\\"Simpson 1/3\\\" rule and the trapezoidal rule, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOT THE SIMPLE ONES\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, calculate the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$$ \\\\int_{a}^{b} lnx \\\\ dx $$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFurther explanations:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1)the limits(a,b) will be given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2)The number of subspaces(n) of [a,b] will also be given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3)I1 is the integral of the Simpson rule. I2 the integral of the trapezoidal rule.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4)ROUND THE RESULTS TO 4 DECIMAL PLACES!!!!!!!!!!!!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGOOD LUCK!!!!!!!!!!!!!!!!!!!!!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61460,"title":"Calculate integrals using numerical methods 2.","description":"Calculate the following integral(I) using the SIMPLE(thus n =1) trapezoidal rule:\r\n\r\nThe llimits(a,b) of the integral will be given.\r\nGOOD LUCK!!!!!!!!!!!!!!!!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 136px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 68px; transform-origin: 469px 68px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the following integral(I) using the SIMPLE(thus n =1) trapezoidal rule:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 23px; text-align: left; transform-origin: 445px 23px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"vertical-align:-19px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"84.5\" height=\"46\" style=\"width: 84.5px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe llimits(a,b) of the integral will be given.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!!!!!!!!!!!!!!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function I = TRAPEZOIDAL(a,b)\r\n  \r\nend","test_suite":"%%\r\na = 0;\r\nb = 6;\r\ny_correct = 18*exp(6);\r\nassert(abs(TRAPEZOIDAL(a,b)-y_correct)\u003c1e4)\r\n%%\r\na = 8;\r\nb = 19;\r\ny_correct = 5.5 *(8*exp(8) + 19*exp(19));\r\nassert(isequal(TRAPEZOIDAL(a,b),y_correct))\r\n%%\r\na = -100;\r\nb = -1;\r\ny_correct = 49.5*(-100*exp(-100) - exp(-1));\r\nassert(isequal(TRAPEZOIDAL(a,b),y_correct))\r\n%%\r\ncode = fileread(which('TRAPEZOIDAL'));\r\nhas_if = ~isempty(regexp(code, '\\bif\\b', 'once'));\r\nassert(~has_if, 'Using \"if\" is not allowed!')","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5158730,"edited_by":5158730,"edited_at":"2026-08-30T13:02:06.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-08-30T11:47:44.000Z","updated_at":"2026-08-31T15:09:49.000Z","published_at":"2026-08-30T11:47:44.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the following integral(I) using the SIMPLE(thus n =1) trapezoidal rule:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$$ \\\\int_{a}^{b} x*e^x \\\\ dx $$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe llimits(a,b) of the integral will be given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGOOD LUCK!!!!!!!!!!!!!!!!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"problems":[{"id":61461,"title":"Calculate integrals using numerical methods 3.","description":"Now let's compare the 2 previous rules. Using the \"Simpson 1/3\" rule and the trapezoidal rule, NOT THE SIMPLE ONES, calculate the following integral:\r\n\r\nFurther explanations:\r\n1)the limits(a,b) will be given.\r\n2)The number of subspaces(n) of [a,b] will also be given.\r\n3)I1 is the integral of the Simpson rule. I2 the integral of the trapezoidal rule.\r\n4)ROUND THE RESULTS TO 4 DECIMAL PLACES!!!!!!!!!!!!\r\nGOOD LUCK!!!!!!!!!!!!!!!!!!!!!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 277px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 138.5px; transform-origin: 469px 138.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 21px; text-align: left; transform-origin: 445px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNow let's compare the 2 previous rules. Using the \"Simpson 1/3\" rule and the trapezoidal rule, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eNOT THE SIMPLE ONES\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, calculate the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 23px; text-align: left; transform-origin: 445px 23px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"vertical-align:-19px\"\u003e\u003cimg 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LEfxvJBJXvof06umwRXiROHMrE+kPB5ot4ru7yh3O50+SYOpgeYefdTR/yMiNI1QOct+7P9PaLZL2+ubR8jbDc/fEz+/YMGCfmajo8Aru3btuoL4+P7+/i9u2bLlBZQ+QFrhjaSXGJ3vY7bKdPe2aUgTQ+gTQBD8dldiYGBA/XAL+M8BhSewYxO6r8Tmk+bNm7dDlxoyqjjAaSwRrn2lVrtaW2FwLfB1nrJU7UH+AGVvAQ8NmpCjhExCalpgRGrE+fd34NXCKqsIirmErC7s6Xtv82gkOYEU7KejLiJ9EY1gb1u1LdYI3Mbs+EsxBsA0rHWLPwtQ7jgaVNvQSer8HLK2IedZGlWd/wHK/NXoxvp3cuHVzkg7klUMpHWk/478TzBbxW6ryXMO6NYhWTCTXI+zXosNt2LbvdhzM4K08yLyXgPv19H9DuAmLqH/S3onvM+S+d/Atds4eCPWJUefSxsHVzvcQaxL0e04+a/AGyHkKA2qA4KRjfUJ7MHUDtqJkN3/zLbxm1ijXdggDTnEKLlUowiaZx/EjQwHjAAAB15JREFU0Zg/piNDI8iUvxvNU5TVvaK1nK18jk7ReUnwENBjlD0f+mRwXedc4z7kfw/QLKV12/v9fAhFA6eqD9DhF6JTnTgfuz6OzJVcYs+iXvrerkAOqdPj7+DQFy5evHgH/Jo1dKq8hzIXG16Keh62ybn+icSL8DHR1K6186H7IbejMAK1/QvWJ/7U7kss7Sf7LNKqemJi4ks0hI7PF1P5KxklwWj02MbvJu90oALfpZTFJ/i1AvRbJ8bH++BZAtxO1kHiSeA0oBc4E54J6I0gB4P+58DhwNvQu7mRWRyp4Sz3oPNkZEv/fOI/pS66z6ROv5v0XEB1vhnn36utPunLgT7KLcMezUqhupL3j8B85QMaXKF8mZ3bUZhWdV30r5O1Wm3D5s2bn5PAUsD3kYitpYjuNiF+VbvBqBRDQo6SwhuqDlNg59Ynvx0+4rdn11Q1xZCQo6Tw+hXTj7Z9XOu09VSytPWJhHU9ZBlNeSrTafl5bKJMyFFIOwWu9Xpl9I3GsZrrk1IrWaowp3o5MZlKO/HmYeq0/IhNbu3s5Ci2KOGsT3Q8fZxw9D7aWJ+UWslShWHmzAbTVjNrRKx2t3auO0pKLWxRwlmfNO6PsJDVdlBkY0aKMMM1LVERU4qUjamc1UAxud1PqjtKhlq0rE/0Dw2C00BT2wzCTImORUVMKVI2qUK+8/k/SRxdS687SlvzwhUL1iemyLbe3l6d6pnkbI3CdexYLXzn839SVbhY5MKTqsiRwcFRwhUL1idGfnN9Yghe5jtGXhf8hetYxKCyOs/FIp+nLIVJlTbyHRwlLKH9+kS8vvlC2oLR35bHz0xhTMn2Rdg/Ef4IwebOjretfYq4tqa0zUwRXCTbVCjqKG0Malmf7OG+h+455DLD6E8vm8KYku3Lt6sU4Y8Q/CIz8tPWlKTMJHrJNYg6ShvF3GfQ/Z3g+Y0x1ieRRwtd7bM7z7VMIl+KsDZVShQ5XRkpppdqRhFdUUdpYxqnsXqu0n8+FrbYRwuhWyHZtFI7r1RhlvnTgE6n6UV0ZXIU2k2fLddzGnqOIfJoIfktwTYt2WlaCh1KdmELWI6S3JHK0fqEw7Xg/eIc93dsp7FbQtJJmwgsJrTNjOHPTuq8huw2dVMJy1GSOtLzn8mxz0+4BD2wb98+/xmI4pUxek0UL69tZnyRjNTOa8ho0Iyzh4eO5She2xMQzk+C508OMrP8mx6K8Tr8FzY1h7LCAnLonKEi5Vc1PHRCjhLOsmoMinMEL0I9xrZYj/pBbQklW9vOnhbN8UlnAcZwE8ULM1QXnqysGWQa0ZHIuaqRkm6EkKOYInq94KODg4NPDA0NfV5rE3A9VqDvbej9lpvHxsb0ULFht6IUa5G3AFl/CJwPLAHOHhhYoQegLCEzgRrDTdTWAhceI8CZ1ZnRCJ6BKOIow8PDb2L20GsJSzmF9b+PQfpd2KZLz5cXLlyoZypJugd9qAWnuBp5ayn19MGDB3VQ9yPwdZVKVe/7gjqEEkZeREsnZEaUzH5CxFGmpqbkHPOpml7KvpNDtr9g8frpmlf7an9//1V6WJc856BZpK+v71+QcVG1Wv3g+Pj4o/pCIc6nl7ifqVZ7Gt/vaAhN6rxOjLwSZNrm2nijPo5IkbKOKsJsGRRGHKVarerR/q8hsY+1yDfp4AvBL5gYn7hMT5iDOwe9uohDfIZt0/nMJldxyfI/q4Az6lWPxQiaRJ++7gNqhRI6z5LWcdQ218azKi5SNqsunz+DwoijbN269deM+g8Aeux/PunzwHWZyCDWN8PbtWvXCNjFXsX7kXnfhaTncenRi1V6J/jBxtNxfk7On8jIiBByCp6mYrPA3IijlNU0IyMjvcwmlyBPbxLeac1GelXzz6DrAzV6qy6zA1I2HCISIoQwf7elZoG5HXMUzllew2XrDJzlaWK9bup3z6pVq9aA6IWrZ7i0lXRoh8RCYQYKF5lFipTNWdWOOQoOoi31UTjJfhxCrzl6Wthy2bmZs17lTZK3F9q7sV3vvRLNcJjODjCzSC6VpmxSa+WSmSTM0J0cJY9ijvi1SNXbg/ps5klsu5fjPLehl8tNRfRncJorcRZ9T0TnM2QVC3nsDGlM6YAQbyNRTGsulQ3d8Ug5MsP1cnKUPIq59OjTC9dRlT3AWnY9XyW+mfjbxHrbX99W+y47oftJlxLy2Flc8cxoLW53moRwvZwcJU1kUj47pq+xY9IL3nrRW99bfZRzmY3Q9M3VQWJ9pyRsUZKwbqGHB1ouq0oQ0dRbqrCm2Faso47SquxVkTZuXaR/jIhymqNUYckmWY6StepZ+ZONcM6JURlDchbnzBijJKl/Ylid1WRlnE5dlqPEVL2tJYa/LU/Wqtv8MYKNSpsrhmRnl4M7K6lwCF2OShcpzmZ5Xry4mCaOZ/TC38KPMLlY4sITEexC6JhgF+Wl81QsiTZukacfzdDE1oySZGfOauUslmTF7KAnt7ydY+Ozo15eyozi1yJntfxiFV/CoZ+cLdBFzfcbAAAA//+D17IhAAAABklEQVQDAJT7CTNTw1vzAAAAAElFTkSuQmCC\" width=\"69\" height=\"46\" style=\"width: 69px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFurther explanations:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1)the limits(a,b) will be given.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2)The number of subspaces(n) of [a,b] will also be given.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3)I1 is the integral of the Simpson rule. I2 the integral of the trapezoidal rule.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4)ROUND THE RESULTS TO 4 DECIMAL PLACES!!!!!!!!!!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!!!!!!!!!!!!!!!!!!!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [I1 I2] = CompareS_T(a,b,n)\r\n    \r\nend ","test_suite":"%%\r\na = 1; \r\nb = 5; \r\nn = 2;\r\nI1_correct = round(2/3*log(405),4);\r\nI2_correct = round(log(45),4);\r\n[I1, I2] = CompareS_T(a,b,n);\r\nassert(abs(I1 - I1_correct) \u003c 1e-4 \u0026\u0026 abs(I2 - I2_correct) \u003c 1e-4)\r\n%%\r\na = 2; \r\nb = 8; \r\nn = 4;\r\nI1_correct = 9.2449;\r\nI2_correct = 9.1804;\r\n[I1, I2] = CompareS_T(a,b,n);\r\nassert(abs(I1 - I1_correct) \u003c 1e-4 \u0026\u0026 abs(I2 - I2_correct) \u003c 1e-6)\r\n%%\r\na = 5;\r\nb = 15;\r\nn = 8;\r\nI1_correct = 22.5734;\r\nI2_correct = 22.5563;\r\n[I1, I2] = CompareS_T(a,b,n);\r\nassert(abs(I1 - I1_correct) \u003c 1e-4 \u0026\u0026 abs(I2 - I2_correct) \u003c 1e-6)\r\n%%\r\ncode = fileread(which('CompareS_T'));\r\nhas_if = ~isempty(regexp(code, '\\bif\\b', 'once'));\r\nassert(~has_if, 'Using \"if\" is not allowed!')","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5158730,"edited_by":5158730,"edited_at":"2026-08-30T13:00:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2026-08-30T13:00:07.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-08-30T12:55:50.000Z","updated_at":"2026-08-31T15:31:58.000Z","published_at":"2026-08-30T13:00:07.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNow let's compare the 2 previous rules. Using the \\\"Simpson 1/3\\\" rule and the trapezoidal rule, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOT THE SIMPLE ONES\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, calculate the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$$ \\\\int_{a}^{b} lnx \\\\ dx $$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFurther explanations:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1)the limits(a,b) will be given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2)The number of subspaces(n) of [a,b] will also be given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3)I1 is the integral of the Simpson rule. I2 the integral of the trapezoidal rule.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4)ROUND THE RESULTS TO 4 DECIMAL PLACES!!!!!!!!!!!!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGOOD LUCK!!!!!!!!!!!!!!!!!!!!!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61460,"title":"Calculate integrals using numerical methods 2.","description":"Calculate the following integral(I) using the SIMPLE(thus n =1) trapezoidal rule:\r\n\r\nThe llimits(a,b) of the integral will be given.\r\nGOOD LUCK!!!!!!!!!!!!!!!!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 136px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 68px; transform-origin: 469px 68px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the following integral(I) using the SIMPLE(thus n =1) trapezoidal rule:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 23px; text-align: left; transform-origin: 445px 23px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"vertical-align:-19px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"84.5\" height=\"46\" style=\"width: 84.5px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe llimits(a,b) of the integral will be given.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!!!!!!!!!!!!!!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function I = TRAPEZOIDAL(a,b)\r\n  \r\nend","test_suite":"%%\r\na = 0;\r\nb = 6;\r\ny_correct = 18*exp(6);\r\nassert(abs(TRAPEZOIDAL(a,b)-y_correct)\u003c1e4)\r\n%%\r\na = 8;\r\nb = 19;\r\ny_correct = 5.5 *(8*exp(8) + 19*exp(19));\r\nassert(isequal(TRAPEZOIDAL(a,b),y_correct))\r\n%%\r\na = -100;\r\nb = -1;\r\ny_correct = 49.5*(-100*exp(-100) - exp(-1));\r\nassert(isequal(TRAPEZOIDAL(a,b),y_correct))\r\n%%\r\ncode = fileread(which('TRAPEZOIDAL'));\r\nhas_if = ~isempty(regexp(code, '\\bif\\b', 'once'));\r\nassert(~has_if, 'Using \"if\" is not allowed!')","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5158730,"edited_by":5158730,"edited_at":"2026-08-30T13:02:06.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-08-30T11:47:44.000Z","updated_at":"2026-08-31T15:09:49.000Z","published_at":"2026-08-30T11:47:44.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the following integral(I) using the SIMPLE(thus n =1) trapezoidal rule:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$$ \\\\int_{a}^{b} x*e^x \\\\ dx $$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe llimits(a,b) of the integral will be given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGOOD LUCK!!!!!!!!!!!!!!!!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"errors":[],"facets":[[],[{"value":"medium","count":2,"selected":false}]],"term":"tag:\"integrals\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}