MATLAB: Suprising results using matlabs quad to solve a simple double definite integral.

Question

Hi everyone, i have a complex function which i have written a matlab function to execute, but before that i did a simple example of definite integral of the form

int_0^1 log int_0^1 x+y dxdy .(here 'int' is the integral sign, underscore 0 hat 1 are the limits of integration, done w.r.t x and y)

doing this by pen and paper gives me -1.33333… but using this code below.i get a wrong answer.

function z1=intlog(y)
%intlog is a function executing the inner integral with respect to %x.
         n=length(y);
          z=zeros(size(y));
for j=1:n
a=0;b=1;
h=@(x) (x+y(j));
z(j)=quad(h,a,b);
z1=log(z);
end

to run this write in command window:

q=quad(@intlog,0,1)

which gives me a wrong answer. any explanation for this. I am using matlab release 2009a.

Thanks in anticipation.

Answer 1

Your pen and paper solution is incorrect. The correct analytic answer is 3*ln(3)/2 - ln(2) - 1 ~= -0.0452, which is spot-on with your code. [Here "ln" is natural log.]