Explain in an itemized fashion (preferably with an example) how one can estimate double integrals over non-rectangular domains.

Explain in an itemized fashion (preferably with an example) how one can estimate double integrals over non-rectangular domains.

Answer 1

[Bjorn Gustavsson]

Read the help for integral2:

Example:

Integrate 1./(sqrt(x+y).*(1+x+y).^2 over the triangle 0 <= x <= 1,

0 <= y <= 1-x. The integrand is infinite at (0,0). The true value of

the integral is pi/4 - 1/2.

fun = @(x,y) 1./( sqrt(x + y) .* (1 + x + y).^2 )

% In Cartesian coordinates:

ymax = @(x) 1 - x

Q = integral2(fun,0,1,0,ymax)

That should give you a good place to start.

HTH