Help in solving an integral using MATLAB

[EDIT: Thu Jun 23 15:48:04 UTC 2011 - Clarify - MKF]

This is the integral that I'm trying to solve.

clear
clc
syms x y;
f = input('Write function = ');
F = inline (char(f));
a = input ('from (x): ');
b = input ('to (x) : ');
a1 = input ('from (y) : ');
b1 = input ('to (y) : ');
F = int (int(f,x,a,b),y,a1,b1);

the function is:

(1/((3.11e-6)-((2.25e-6)*(((1-((x^2)/(1e-8)))^2)*((1-((y^2)/(1e-8)))^2)*(1+((1.1e-8)*(x^2))+((1.1e-8)*(y^2)))))))

and must be evaluate in x: from -1e-4 to 1e-4 and in y from -1e-4 to 1e-4

Answer 1

[Matt Fig]

f = @(x,y)(1./((3.11e-6)-((2.25e-6).*(((1-((x.^2)./(1e-8))).^2).*((1-((y.^2)./(1e-8))).^2).*(1+((1.1e-8).*(x.^2))+((1.1e-8).*(y.^2)))))))

dblquad(f,-1e-4,1e-4,-1e-4,1e-4)

Answer 2

[Walter Roberson]

int() applies to symbolic expressions, not to inline functions.

That said: the function is difficult (perhaps impossible) to integrate symbolically, but numeric integration should be fast. Consider using one of the quad* integrators.