How to use "trapz" on a double integral?

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.

[Lia]

In case anyone later comes along to read this post, I think I figured out a way to do the double integral using trapz.

% integration limits
x = linspace(-2,2);
y = linspace (0,3);

% given function
f = (x.^4) - (3*x.*y) + (6.*(y.^2));
q =  x.^4 - x;

% implement trapezoidal rule
I = trapz(x,q.*trapz(y,f))

I don't know if it is right, but hopefully it will get you on the right track.

[Jess]

Was it right?

[Torsten]

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

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

Best wishes

Torsten.

Answer 1

[John BG]

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

Answer 2

[Sean de Wolski]

Instead of using trapz, try integral2().

doc integral2

If you are on an olde release that does not have integral2, try dblquad.

doc dblquad

[Lia]

I appreciate it, but my prof calls for the use of trapz