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

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friet 2016년 11월 29일
댓글: Star Strider 2016년 12월 12일
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

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### 채택된 답변

Star Strider 2016년 11월 29일
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.
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Star Strider 2016년 12월 12일
Thank you!

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