Find the volume of solid generated by revolving the region bounded by the curve 𝑦 = √𝑥, 𝑦 = 0, 𝑥 = 2 about the line 𝑦 = 5.
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Find the volume of solid generated by revolving the region bounded by the curve 𝑦 = √𝑥, 𝑦 = 0, 𝑥 = 2 about the line 𝑦 = 5.
2 件のコメント
Nithish
2023 年 1 月 17 日
%Evaluation of Volume of solid of revolution
clear
clc
syms x
f(x)=sqrt(x); % Given function
yr=5; % Axis of revolution y=yr
I=[0,2]; % Interval of integration
a=I(1);b=I(2);
vol=pi*int((yr-f(x))^2,a,b);
disp('Volume of solid of revolution is: ');
disp(vol); % Visualization if solid of revolution
fx=matlabFunction(f);
xv = linspace(a,b,101); % Creates 101 points from a to b
[X,Y,Z] = cylinder(fx(xv)-yr);
Z = a+Z.*(b-a); % Extending the default unit height of the
%cylinder profile to the interval of integration.
surf(Z,Y+yr,X) % Plotting the solid of revolution about y=yr
hold on;
plot([a b],[yr yr],'-r','LineWidth',2); % Plotting the line y=yr
view(22,11); % 3-D graph viewpoint specification
xlabel('X-axis');ylabel('Y-axis');zlabel('Z-axis');
採用された回答
Image Analyst
2022 年 1 月 2 日
編集済み: Image Analyst
2022 年 1 月 2 日
x = linspace(0, 30, 1000);
y = sqrt(x);
plot(x, y, 'b-');
grid on;
yline(0, 'Color', 'g', 'LineWidth', 2);
yline(5, 'Color', 'g', 'LineWidth', 2);
xline(2, 'Color', 'g', 'LineWidth', 2);
text(5, 4, 'Not this region', 'Color', 'r', 'FontSize', 15)
text(11, 2.5, 'Spin this region', 'Color', 'r', 'FontSize', 15)
You need to actually specify both ends of x.
Is x1=0 and x2=2, or is x1=2 and x2 = 25?
その他の回答 (1 件)
John D'Errico
2022 年 1 月 2 日
編集済み: John D'Errico
2022 年 1 月 2 日
Ok. I did it. Not too hard. Oh. Wait. Was this YOUR homework assignment, given to you? Is there a reason why we should do it for you?
Please stop posting your homework assignment questions. They were assigned to you, not to us. Unless, of course, you are willing to give us the name and address of your teacher. Then we can send in the solution directly to them, and get credit for ourselves.
Homework is given to teach you. In this case, it would teach you both MATLAB and mathematics, but only if you make an effort. Your brain is a muscle. Exercise it, and it will get stronger.
Note: Had you made an effort, I would have offered help, to a degree proportional to the effort you made. Having shown no effort, I'll tell you only that it took about 20 seconds to write the very few lines of code I used to solve this. (If you count the line syms x y, 3 lines in total.) So in a sense, I did give you help, since I gave you the very first line of code I used.
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