Numerical double Integral on triangular domain

Hi everyone,

I'm trying to compute the integral of a function f(x,y) over a triangular domain given by 4 < x <8 and 4-x < y < 0. f(x,y) is a n x n matrix where y varies over the rows and x over the lines. The code I wrote does the job :

x=linspace(4,8,n);
endpt=x-4;                          % Gives the lower bound for the allowed region of y         

for i=1:n
    y(:,i)=linspace(0,endpt(i),n);  % Each row j of this matrix contains all allowed values of y for a given value of x i.e 4-x(j) < y < 0.
end

for i=n
    y_int(i)=trapz(y(:,i),f(:,i));  % Each iteration integrates the rows of f from 0 to 4-x(i)
end

final_int = trapz (x,-y_int);       % Integration over the domain of x (notice the - sign to account for the fact we are integrating above from 0 down to 4-x(j).)

However, I would like to know if it is possible to write the same computation using the cumtrapz function of matlab in order to avoid the second loop (the n integrations) ? I tried something like this but it doesn't work ... Thank you for your help !

t1=linspace(-4,0,n1);

res=cumtrapz(t1,f,2);

trapz(s1,-diag(res))

Answer 1

[vincenzo scarnera]

I want to do it on a spherical domain

[darova]

PLease create your own question