How can I calculate the area under a graph (Shaded area)?

Hello,

I am trying to calculate the area of the shaded area shown in the graph. This is my Matlab code. When I use trapz keyword it gives me the whole area. Is there any way to calculate the shaded area 1 and area 2 which are separated by the dotted lines.

clear all
clc
close all

x=0:0.1:3.14;
y=sin(4*x).*sec(3*x);

yy = zeros(1,length(x));
yy(:) = 0;

y1=-20:0.1:20;
x1 = ones(1,length(y1));
x1(:) = 0.5;

plot(x,y,x,yy,'--',x1,y1,'--')
trapx(x,y)

Is there also any way to select area 1 and paint it with different colors using matlab code.

Thanks

Answer 1

[Star Strider]

Try this:

x=0:0.1:3.14;
y=sin(4*x).*sec(3*x);

yy = zeros(1,length(x));
yy(:) = 0;

y1=-20:0.1:20;
x1 = ones(1,length(y1));
x1(:) = 0.5;

area_1 = trapz(x(x<=0.5), y(x<=0.5));                       % Calculate ‘Area #1’ 
xc = find((y .* circshift(y, [0 1])) < 0);                  % Define ‘y’ Zero-Crossings
idx_rng = xc(1)-1:xc(1);                                    % Index Range Including Zero-Crossing
x0 = interp1(y(xc(1)-1:xc(1)), x(xc(1)-1:xc(1)), 0);        % Find ‘x’ At Zero Crossing
area_2 = trapz([0.5  x0], [y(x == 0.5) 0]);                 % Calculate ‘Area #2’

plot(x,y,x,yy,'--',x1,y1,'--')
hold on
ha1 = area(x(x<=0.5), y(x<=0.5), 'FaceColor','g');
ha2 = area([0.5  x0], [y(x == 0.5) 0], 'FaceColor','r');
hold off
A1str = sprintf('Area 1 = %6.3f', area_1);
A2str = sprintf('Area 2 = %6.3f', area_2);
legend([ha1 ha2], A1str, A2str)

I colored ‘area2’ for clarity, and to show the value in the legend. Make whatever changes you need to. Note that this code is specific to your Question as you posted it, and while the ideas will generalise to similar applications, the code itself will not.

[friet]

Thank you very much

clear all

x=0:0.1:3.14;
y=sin(4*x).*sec(3*x);
yy = zeros(1,length(x));
yy(:) = 0;
y1=-20:0.1:20;
x1 = ones(1,length(y1));
x1(:) = 0.5;

area_1 = trapz(x(x<=0.5), y(x<=0.5));                       % Calculate ‘Area #1’ 
xc = find((y .* circshift(y, [0 1])) < 0);                  % Define ‘y’ Zero-Crossings
idx_rng = xc(1)-1:xc(1);                                    % Index Range Including Zero-Crossing
x0 = interp1(y(xc(1)-1:xc(1)), x(xc(1)-1:xc(1)), 0);        % Find ‘x’ At Zero Crossing
area_2 = trapz([0.5  x0], [y(x == 0.5) 0]);                 % Calculate ‘Area #2’
plot(x,y,x,yy,'--',x1,y1,'--')
hold on
ha1 = area(x(x<=0.5), y(x<=0.5), 'FaceColor','g');
ha2 = area([0.5  x0], [y(x == 0.5) 0], 'FaceColor','r');
hold off
A1str = sprintf('Area 1 = %6.3f', area_1);
A2str = sprintf('Area 2 = %6.3f', area_2);
legend([ha1 ha2], A1str, A2str)

x01 = interp1(y(xc(2)-1:xc(2)), x(xc(2)-1:xc(2)), 0); 
area_3= trapz([0.5812  x01], [y(x == 0.5) 1]);  

figure(3)
plot(x,y,x,yy,'--',x1,y1,'--')
hold on
ha1 = area(x(x<=0.5), y(x<=0.5), 'FaceColor','g');
ha2 = area([0.5  x0], [y(x == 0.5) 0], 'FaceColor','r');
ha3=area([0.5812  x01], [y(x == 0.5) 0], 'FaceColor','b');
hold off
A1str = sprintf('Area 1 = %6.3f', area_1);
A2str = sprintf('Area 2 = %6.3f', area_2);
A3str = sprintf('Area 3 = %6.3f', area_3);
legend([ha1 ha2 ha3], A1str, A2str, A3str)

I am continuing to work to find area 3, as shown in the figure.

I am able to trace the zero crossing in x axis however I cant fins the right data points on the y-axis. Can you help me. Thank you!!

[Star Strider]

My pleasure!

The y-values at the zero-crossings are by definition zero. You only really need the zero-crossing x-values to calculate the integrals of the segments between the zero-crossings. Use the trapz function for those.

A little utility function I wrote to find the approximate zero-crossing indices may be helpful:

zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);                    % Returns Approximate Zero-Crossing Indices Of Argument Vector

Use this with your y-data vector.

[friet]

So Area 3 should be?

area_3= trapz([0.5812  x01], [y(x == 0.5) 1]);

[Star Strider]

I couldn’t figure out your ‘area_3’ calculation, so I changed the code just a bit to make the calculations easier:

x=0:0.1:3.14;
yf = @(x) sin(4*x).*sec(3*x);                               % Create Anonymous Function
y = yf(x);

yy = zeros(1,length(x));
yy(:) = 0;

y1=-20:0.1:20;
x1 = ones(1,length(y1));
x1(:) = 0.5;

area_1 = trapz(x(x<=0.5), y(x<=0.5));                       % Calculate ‘Area #1’ 
xc = find((y .* circshift(y, [0 1])) < 0);                  % Define ‘y’ Zero-Crossings
idx_rng = xc(1)-1:xc(1);                                    % Index Range Including Zero-Crossing
x0 = interp1(y(xc(1)-1:xc(1)), x(xc(1)-1:xc(1)), 0);        % Find ‘x’ At Zero Crossing
area_2 = trapz([0.5  x0], [y(x == 0.5) 0]);                 % Calculate ‘Area #2’

for k1 = 1:length(xc)
    ix_rng = xc(k1)-1:xc(k1);                               % Index Range
    x0v(k1) = interp1(y(ix_rng), x(ix_rng), 0);             % Interpolate
end
for k1 = 1:length(x0v)-1
    area_(k1) = integral(yf, x0v(k1), x0v(k1+1));           % Integrate Using ‘integral’
end

plot(x,y,x,yy,'--',x1,y1,'--')
hold on
ha1 = area(x(x<=0.5), y(x<=0.5), 'FaceColor','g');
ha2 = area([0.5  x0], [y(x == 0.5) 0], 'FaceColor','r');
hold off
A1str = sprintf('Area 1 = %6.3f', area_1);
A2str = sprintf('Area 2 = %6.3f', area_2);
legend([ha1 ha2], A1str, A2str)

The changes aren’t plotted. The ‘area_()’ vector contains in order: ‘area_3’, ‘area_4’, and ‘area_5’+‘area_6’. You will have to insert the line that separates the last two in order to calculate the integrals separately. (I don’t see it.) It should be inserted just before the last element that I calculate in ‘x0v’. You will probably have to do that manually (that is, specifically code for it). That is straightforward to do.

Example:

old_vector = 1:5;
new_vector([1:length(old_vector)-1 length(old_vector)+1]) = old_vector;
new_vector(end-1) = pi;

producing:

old_vector =
     1     2     3     4     5

new_vector =
            1            2            3            4       3.1416            5

Make the appropriate changes to do something similar for ‘x0v’.

[friet]

Thank you very much I try to update the area, However I am getting something wrong. Can you please check my code below.

clear all
clc

% Create Anonymous Function

x=0:0.1:3.14;
yf = @(x) sin(4*x).*sec(3*x);                               
y = yf(x);
yy = zeros(1,length(x));
yy(:) = 0;
y1=-20:0.1:20;
x1 = ones(1,length(y1));
x1(:) = 0.5;
x2 = ones(1,length(y1));
x2(:) = 2.6;

figure(1)
plot(x,y,x,yy,x1,y1,'--',x2,y1,'--')

%Area calculation

area_1 = trapz(x(x<=0.5), y(x<=0.5));                       % Calculate ‘Area #1’ 
% area_1= integral(yf, 0, 0.5);              Why this dont work

xc = find((y .* circshift(y, [0 1])) < 0);
x0 = interp1(y(xc(1)-1:xc(1)), x(xc(1)-1:xc(1)), 0);        % Find ‘x’ At Zero Crossing
area_2 = trapz([0.5  x0], [y(x == 0.5) 0]);
%
for k1 = 1:length(xc)
    ix_rng = xc(k1)-1:xc(k1);                               % Index Range
    x0v(k1) = interp1(y(ix_rng), x(ix_rng), 0);             % Interpolate
end
%

area_3= integral(yf, x0v(1), x0v(2));
area_4= integral(yf, x0v(2), x0v(3));
area_5= integral(yf, x0v(3), 2.6);
area_6= integral(yf, 2.6, x0v(4));

%Postprocessing

figure(2)

plot(x,y,x,yy,'--',x1,y1,'--',x2,y1,'--')
hold on
hold on
ha1 = area(x(x<=0.5), y(x<=0.5), 'FaceColor','g');
ha2 = area([0.5  x0], [y(x == 0.5) 0], 'FaceColor','r');
ha3 = area([x0 x0v(2)],[y(x == 0.5) 0], 'FaceColor','b');
ha4 = area([x0v(1) x0v(2)],[y(x == x0v(2)) 0], 'FaceColor','k');
ha5 = area([x0v(3) 2.6],[y(x == x0v(3)) 0], 'FaceColor','y');
ha6 = area([2.6 x0v(4)],[y(x == x0v(3)) 0], 'FaceColor','c');
hold off
A1str = sprintf('Area 1 = %6.3f', area_1);
A2str = sprintf('Area 2 = %6.3f', area_2);
A3str = sprintf('Area 3 = %6.3f', area_3);
A4str = sprintf('Area 4 = %6.3f', area_4);
A5str = sprintf('Area 5 = %6.3f', area_5);
A6str = sprintf('Area 6 = %6.3f', area_6);
legend([ha1 ha2 ha3 ha4 ha5 ha6], A1str, A2str, A3str, A4str, A5str, A6str)

And other question i have is why

area_1= integral(yf, 0, 0.5); 

|is not giving me the same answer as|

area_1 = trapz(x(x<=0.5), y(x<=0.5));

[Star Strider]

My newest code doesn’t start at ‘area_1’. The loop starts at ‘area_3’. The values for ‘area_1’ and ‘area_2’ should be as they were before.

[friet]

I didnt change anything from Area1 and Area 2. However why the area plot don't make sense in my plot.

[Star Strider]

It is very late here, so I decided to make this easier for me. You can change the resolution by changing the number of elements in ‘x’.

The Code —

N = 100;                                                        % Number Of Elements In ‘x’
x = linspace(0, pi);
yf = @(x) sin(4*x).*sec(3*x);                                   % Create Anonymous Function
y = yf(x);

zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);            % Returns Approximate Zero-Crossing Indices Of Argument Vector
xc = zci(y);                                                    % Zero-Crossings
[~,ixp] = findpeaks(y, 'MinPeakHeight',5);                      % Positive Peak Location Indices
[~,ixn] = findpeaks(-y);                                        % Negative Peak Locations
ixs = unique([xc(:)',ixp(:)',ixn(:)']);                         % Sorted Indices (Ascending)

for k1 = 1:length(ixs)-1                                        % Loop Through Sorted Indices
    area_(k1) = integral(yf, x(ixs(k1)), x(ixs(k1+1)));         % Integrate Using ‘integral’
end

fprintf(1, '\n\tArea Segments —\n')
for k1 = 1:length(area_)                            
    fprintf(1,'\t\tArea %d = %8.4f\n',k1, area_(k1))            % Print Area Segments
    legstr{k1} = sprintf('Area %d = %8.4f\n',k1, area_(k1));    % Create Legend Strings
end

cm = colormap(jet(length(area_)));                              % Color Map For Patches

figure(1)
plot(x, y)                                                      % Plot Function
hold on
for k1 = 1:length(area_)                                        % Plot Patches
    ixv = [ixs(k1):ixs(k1+1)];                                  % Index Range
    hp{k1} = patch([x(ixv) flip(x(ixv))], [yf(x(ixv)) zeros(size(flip(x(ixv))))], cm(k1,:));
end
legend([hp{:}], legstr, 'Location','N')                         % Legend

The patch calls are straightforward to code, but not easy to understand without reading the documentation and doing some experimentation. I will go into them in a bit of detail if you want.

The Plot —

I made some simplifications to make the code work efficiently. This does what you want without all the detailed coding originally required. You may have to enlarge the plot to see ‘Area 2’ and ‘Area 6’, both newly-defined in this code. They don’t correspond exactly to your original description, but the code works, and tonight that’s good enough for me. I comment-documented all but the patch call (that seems to be incidental anyway).

[friet]

Thanks

What about when I have datapoints instead of arbitrary equation I try below, However the integral function dont work. Can you help me. Thanks

    clear all
    close all
    clc

    x=[-64.8138
    -63.9828
    -63.1519
    -62.3209
    -61.4900
    -60.6590
    -59.8281
    -58.9971
    -58.1662
    -57.3352
    -56.5043
    -55.6734
    -54.8424
    -54.0115
    -53.1805
    -52.3496
    -51.5186
    -50.6877
    -49.8567
    -49.0258
    -48.1948
    -47.3639
    -46.5330
    -45.7020
    -44.8711
    -44.0401
    -43.2092
    -42.3782
    -41.5473
    -40.7163
    -39.8854
    -39.0544
    -38.2235
    -37.3926
    -36.5616
    -35.7307
    -34.8997
    -34.0688
    -33.2378
    -32.4069
    -31.5759
    -30.7450
    -29.9140
    -29.0831
    -28.2521
    -27.4212
    -26.5903
    -25.7593
    -24.9284
    -24.0974
    -23.2665
    -22.4355
    -21.6046
    -20.7736
    -19.9427
    -19.1117
    -18.2808
    -17.4499
    -16.6189
    -15.7880
    -14.9570
    -14.1261
    -13.2951
    -12.4642
    -11.6332
    -10.8023
    -9.9713
    -9.1404
    -8.3095
    -7.4785
    -6.6476
    -5.8166
    -4.9857
    -4.1547
    -3.3238
    -2.4928
    -1.6619
    -0.8309
    0.0000
    0.8309
    1.6619
    2.4928
    3.3238
    4.1547
    4.9857
    5.8166
    6.6476
    7.4785
    8.3095
    9.1404
    9.9713
    10.8023
    11.6332
    12.4642
    13.2951
    14.1261
    14.9570
    15.7880
    16.6189
    17.4499
    18.2808
    19.1117
    19.9427
    20.7736
    21.6046
    22.4355
    23.2665
    24.0974
    24.9284
    25.7593
    26.5903
    27.4212
    28.2521
    29.0831
    29.9140
    30.7450
    31.5759
    32.4069
    33.2378
    34.0688
    34.8997
    35.7307
    36.5616
    37.3926
    38.2235
    39.0544
    39.8854
    40.7163
    41.5473
    42.3782
    43.2092
    44.0401
    44.8711
    45.7020
    46.5330
    47.3639
    48.1948
    49.0258
    49.8567
    50.6877
    51.5186
    52.3496
    53.1805
    54.0115
    54.8424
    55.6734
    56.5043
    57.3352
    58.1662
    58.9971
    59.8281
    60.6590
    61.4900
    62.3209
    63.1519
    63.9828
    64.8138
    65.6447
    66.4756
    67.3066
    68.1375
    68.9685
    69.7994
    70.6304
    71.4613
    72.2923
    73.1232
    73.9542
    74.7851
    75.6160
    76.4470
    77.2779
    78.1089
    78.9398
    79.7708
    80.6017
    81.4327
    82.2636
    83.0946
    83.9255
    84.7564
    85.5874
    86.4183
    87.2493
    88.0802
    88.9112
    89.7421
    90.5731
    91.4040
    92.2350
    93.0659
    93.8968
    94.7278
    95.5587
    96.3897
    97.2206
    98.0516
    98.8825
    99.7135
    100.5444
    101.3754
    102.2063
    103.0372
    103.8682
    104.6991
    105.5301
    106.3610
    107.1920
    108.0229
    108.8539
    109.6848
    110.5158
    111.3467
    112.1777
    113.0086
    113.8395
    114.6705
    115.5014
    116.3324
    117.1633
    117.9943
    118.8252
    119.6562
    120.4871
    121.3181
    122.1490
    122.9799
    123.8109
    124.6418
    125.4728
    126.3037
    127.1347
    127.9656
    128.7966
    129.6275
    130.4585
    131.2894
    132.1203
    132.9513
    133.7822
    134.6132
    135.4441
    136.2751
    137.1060
    137.9370
    138.7679
    139.5989
    140.4298
    141.2607
    142.0917
    142.9226
    143.7536
    144.5845
    145.4155
    146.2464
    147.0774
    147.9083
    148.7393
    149.5702
    150.4011
    151.2321
    152.0630
    152.8940
    153.7249
    154.5559
    155.3868
    156.2178
    157.0487
    157.8797
    158.7106
    159.5415
    160.3725
    161.2034
    162.0344
    162.8653
    163.6963
    164.5272
    165.3582
    166.1891
    167.0201
    167.8510
    168.6819
    169.5129
    170.3438
    171.1748
    172.0057
    172.8367
    173.6676
    174.4986
    175.3295
    176.1605
    176.9914
    177.8223
    178.6533
    179.4842
    180.3152
    181.1461
    181.9771
    182.8080
    183.6390
    184.4699
    185.3009
    186.1318
    186.9628
    187.7937
    188.6246
    189.4556
    190.2865
    191.1175
    191.9484
    192.7794
    193.6103
    194.4413
    195.2722
    196.1032
    196.9341
    197.7650
    198.5960
    199.4269
    200.2579
    201.0888
    201.9198
    202.7507
    203.5817
    204.4126
    205.2436
    206.0745
    206.9054
    207.7364
    208.5673
    209.3983
    210.2292
    211.0602
    211.8911
    212.7221
    213.5530
    214.3840
    215.2149
    216.0458
    216.8768
    217.7077
    218.5387
    219.3696
    220.2006
    221.0315
    221.8625
    222.6934
    223.5244
    224.3553
    225.1862
    226.0172
    226.8481
    227.6791
    228.5100
    229.3410
    230.1719
    231.0029
    231.8338
    232.6648
    233.4957
    234.3266
    235.1576
    235.9885
    236.8195
    237.6504
    238.4814
    239.3123
    240.1433
    240.9742
    241.8052
    242.6361
    243.4670
    244.2980
    245.1289
    245.9599
    246.7908
    247.6218
    248.4527
    249.2837
    250.1146
    250.9456
    251.7765
    252.6074
    253.4384
    254.2693
    255.1003
    255.9312
    256.7622
    257.5931
    258.4241
    259.2550
    260.0860
    260.9169
    261.7479
    262.5788
    263.4097
    264.2407
    265.0716
    265.9026
    266.7335
    267.5645
    268.3954
    269.2264
    270.0573
    270.8883
    271.7192
    272.5501
    273.3811
    274.2120
    275.0430
    275.8739
    276.7049
    277.5358
    278.3668
    279.1977
    280.0287
    280.8596
    281.6905
    282.5215
    283.3524
    284.1834
    285.0143
    285.8453
    286.6762
    287.5072
    288.3381
    289.1691
    290.0000
    290.8309
    291.6619
    292.4928
    293.3238
    294.1547
    294.9857
    295.8166
    296.6476
    297.4785
    298.3095
    299.1404
    299.9713
    300.8023
    301.6332
    302.4642
    303.2951
    304.1261
    304.9570
    305.7880
    306.6189
    307.4499
    308.2808
    309.1117
    309.9427
    310.7736
    311.6046
    312.4355
    313.2665
    314.0974
    314.9284
    315.7593
    316.5903
    317.4212
    318.2521
    319.0831
    319.9140
    320.7450
    321.5759
    322.4069
    323.2378
    324.0688
    324.8997
    325.7307
    326.5616
    327.3926
    328.2235
    329.0544
    329.8854
    330.7163
    331.5473
    332.3782
    333.2092
    334.0401
    334.8711
    335.7020
    336.5330
    337.3639
    338.1948
    339.0258
    339.8567
    340.6877
    341.5186
    342.3496
    343.1805
    344.0115
    344.8424
    345.6734
    346.5043
    347.3352
    348.1662
    348.9971
    349.8281
    350.6590
    351.4900
    352.3209
    353.1519
    353.9828
    354.8138
    355.6447
    356.4756
    357.3066
    358.1375
    358.9685
    359.7994
    360.6304
    361.4613
    362.2923
    363.1232
    363.9542
    364.7851
    365.6160
    366.4470
    367.2779
    368.1089
    368.9398
    369.7708
    370.6017
    371.4327
    372.2636
    373.0946
    373.9255
    374.7564
    375.5874
    376.4183
    377.2493
    378.0802
    378.9112
    379.7421
    380.5731
    381.4040
    382.2350
    383.0659
    383.8968
    384.7278
    385.5587
    386.3897
    387.2206
    388.0516
    388.8825
    389.7135
    390.5444
    391.3754
    392.2063
    393.0372
    393.8682
    394.6991
    395.5301
    396.3610
    397.1920
    398.0229
    398.8539
    399.6848
    400.5158
    401.3467
    402.1777
    403.0086
    403.8395
    404.6705
    405.5014
    406.3324
    407.1633
    407.9943
    408.8252
    409.6562
    410.4871
    411.3181
    412.1490
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    413.8109
    414.6418
    415.4728
    416.3037
    417.1347
    417.9656
    418.7966
    419.6275
    420.4585
    421.2894
    422.1203
    422.9513
    423.7822
    424.6132
    425.4441
    426.2751
    427.1060
    427.9370
    428.7679
    429.5989
    430.4298
    431.2607
    432.0917
    432.9226
    433.7536];

    sf=@(x) [-0.9243
    -0.9691
    -1.0153
    -1.0631
    -1.1128
    -1.1643
    -1.2177
    -1.2737
    -1.3319
    -1.3929
    -1.4565
    -1.5231
    -1.5929
    -1.6660
    -1.7428
    -1.8232
    -1.9077
    -1.9964
    -2.0897
    -2.1877
    -2.2911
    -2.3997
    -2.5142
    -2.6347
    -2.7618
    -2.8959
    -3.0374
    -3.1867
    -3.3442
    -3.5106
    -3.6859
    -3.8710
    -4.0661
    -4.2720
    -4.4887
    -4.7168
    -4.9566
    -5.2085
    -5.4726
    -5.7493
    -6.0386
    -6.3404
    -6.6548
    -6.9815
    -7.3202
    -7.6704
    -8.0317
    -8.4033
    -8.7842
    -9.1735
    -9.5699
    -9.9720
    -10.3784
    -10.7875
    -11.1974
    -11.6061
    -12.0117
    -12.4117
    -12.8042
    -13.1866
    -13.5565
    -13.9116
    -14.2493
    -14.5672
    -14.8629
    -15.1343
    -15.3791
    -15.5953
    -15.7808
    -15.9342
    -16.0538
    -16.1385
    -16.1873
    -16.1994
    -16.1744
    -16.1123
    -16.0131
    -15.8773
    -15.7057
    -15.4992
    -15.2592
    -14.9872
    -14.6851
    -14.3549
    -13.9987
    -13.6190
    -13.2182
    -12.7990
    -12.3640
    -11.9160
    -11.4574
    -10.9914
    -10.5203
    -10.0469
    -9.5734
    -9.1022
    -8.6357
    -8.1756
    -7.7240
    -7.2825
    -6.8525
    -6.4355
    -6.0323
    -5.6439
    -5.2710
    -4.9141
    -4.5736
    -4.2497
    -3.9421
    -3.6512
    -3.3762
    -3.1173
    -2.8737
    -2.6451
    -2.4308
    -2.2302
    -2.0426
    -1.8673
    -1.7037
    -1.5511
    -1.4088
    -1.2760
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    8.5842e-3
    0.0459
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    0.1402
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    1.0066
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    1.6413
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    0.9578
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    0.0416
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    0.6423
    0.7701
    0.9069
    1.0531
    1.2091
    1.3754
    1.5525
    1.7408
    1.9408
    2.1532
    2.3783
    2.6169
    2.8694
    3.1363
    3.4181
    3.7151
    4.0278
    4.3567
    4.7020
    5.0638
    5.4423
    5.8376
    6.2494
    6.6776
    7.1217
    7.5813
    8.0557
    8.5441
    9.0453
    9.5581
    10.0811
    10.6127
    11.1511
    11.6943
    12.2400
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    13.3296
    13.8683
    14.3993
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    16.8340
    17.2554
    17.6480
    18.0089
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    18.6250
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    18.3519
    18.0146
    17.6383
    17.2253
    16.7785
    16.3008
    15.7953
    15.2652
    14.7139
    14.1447
    13.5611
    12.9667
    12.3647
    11.7583
    11.1509
    10.5454
    9.9446
    9.3514
    8.7682
    8.1971
    7.6404
    7.0996
    6.5764
    6.0722
    5.5879
    5.1245
    4.6824
    4.2621
    3.8639
    3.4877
    3.1335
    2.8007
    2.4892
    2.1982
    1.9272
    1.6753
    1.4415
    1.2254
    1.0256
    0.8415
    0.6718
    0.5158
    0.3724
    0.2408
    0.1197
    8.6221e-3
    -0.0934
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    -0.2739
    -0.3538
    -0.4278
    -0.4964
    -0.5603
    -0.6200
    -0.6758
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    -0.7780
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    -0.2563
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    -0.1538
    -0.1238
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    -0.0703
    -0.0472
    -0.0265
    -8.4767e-3
    7.1236e-3
    0.0200
    0.0304
    0.0380
    0.0431
    0.0453
    0.0450
    0.0422
    0.0368
    0.0288
    0.0184
    5.8358e-3
    -9.1550e-3
    -0.0262
    -0.0454
    -0.0664
    -0.0891
    -0.1135
    -0.1396
    -0.1670
    -0.1956
    -0.2254
    -0.2563
    -0.2881
    -0.3206
    -0.3541
    -0.3880
    -0.4226
    -0.4576
    -0.4932
    -0.5292
    -0.5658
    -0.6029
    -0.6404
    -0.6785
    -0.7172
    -0.7567
    -0.7967
    -0.8380
    -0.8802];

    s = sf(x);

    yy = zeros(1,length(x));
    yy(:) = 0;

    y1=-20:0.0666:20;
    x1 = ones(1,length(y1));
    x1(:) = 0;

    y12=-20:0.0666:20;
    x12 = ones(1,length(y1));
    x12(:) = 290;

    plot(x,s,x,yy,'--',x1,y1,'--',x12,y12,'--')

    xc=[79 139,248,363,428];                           % intercept points
    Area1=integral(sf,xc(1), xc(2));
    Area2=integral(sf,xc(2), xc(3));
    Area3=integral(sf,xc(3), xc(4));
    Area4=integral(sf,xc(4), xc(5));

[Star Strider]

Please attach your data as a ‘.mat’ file. That makes it easier for me to load it and use it.

[friet]

Attached

[Star Strider]

This works:

The Code —

D = load('friet data.mat');
x = D.x;
s = D.s;

zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);                        % Returns Approximate Zero-Crossing Indices Of Argument Vector
xc = zci(s);                                                                % Zero-Crossing Indices Of ‘s’
ixv = [xc xc-1];                                                            % Index Range Matrix
for k1 = 1:size(ixv,1)
    xzc(k1) = interp1(s(ixv(k1,:)), x(ixv(k1,:)), 0, 'linear','extrap');    % Interpolated Zero-Crossings
end
[pky,pkix] = findpeaks( s, 'MinPeakHeight',10);                             % Peak & Index
[vly,vlix] = findpeaks(-s, 'MinPeakHeight',10);                             % Valley & Index
% xsrt = sort([xzc x(pkix), x(vlix)]);
ixsrt = sort([xc; pkix; vlix]);                                             % Sort Indices
ixsrt = ixsrt(:)';
xsrt = x(ixsrt);                                                            % Sort ‘x’ Values

for k1 = 1:length(ixsrt)-1
    ixrng = ixsrt(k1):ixsrt(k1+1);
    int_s(k1) = trapz(x(ixrng), s(ixrng));
end

cm = colormap(jet(4));

figure(1)
plot(x, s)
hold on
for k1 = 1:4
    ixrng = [ixsrt(k1):ixsrt(k1+1)]';
    hp{k1} = patch(x([ixrng; flipud(ixrng)])', [s(ixrng); zeros(size(ixrng))]', cm(k1,:));
    lgnd{k1} = sprintf('Area %d = %7.2f', k1, int_s(k1));
end
hold off
grid
legend([hp{:}], lgnd{:}, 'Location','NW')

The Plot —

I also created and attached the ‘.mat’ file of your data.

[friet]

Star Strider! You are the Best!!

[Star Strider]

Thank you!