How to use "trapz" on a double integral?

Question

Lia 2013-4-23

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/73319-how-to-use-trapz-on-a-double-integral

评论： Torsten 2016-1-18

I have a double integral where f = integral (x.^4 - 3*x*y +6*y.^2)dxdy with the outer limits -2 to 2 and the inner limits are 0 to 3. I am supposed to evaluate this integral using Matlab's built in function "trapz" and set the segment width in the x and y- directions at h = 0.1.

Here's what I have so far:

% integration limits
a = -2; b = 3; n = 2;
% given function
f = @(w,y) ((w.^4) - (3*w*y) + (6*(y^2)))
% implement composite trapezoidal rule
trapz(f,a,b)

I know that I am pretty far off from getting the answer, so I apologize and hopefully don't look too dumb.

3 个评论
显示 1更早的评论隐藏 1更早的评论

Jess 2016-1-16

Was it right?

Torsten 2016-1-18

Take a look at the example "Multiple Numerical Integrations" under

http://de.mathworks.com/help/matlab/ref/trapz.html

Best wishes

Torsten.

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Answer 1

John BG 2016-1-17

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/73319-how-to-use-trapz-on-a-double-integral#answer_206415

在 MATLAB Online 中打开

try

x1=-2;dx=.1;x2=2;
y1=0;dy=.1;y2=3
[X,Y]=meshgrid(x1:dx:x2,y1:dy:y2)
Z=X.^4-3*X.*Y+6*Y.^2
x=x1:dx:x2;y=y1:dy:y2
I=trapz(y,trapz(x,Z,2))

you can visualize the curve with

surf(Z)

mind the negative values

find(Z<0)

meaning the curve is not positive for all values in the patch to run the double integral through. If attempting to measure power, square any function. Hope it helps

John