MATLAB Computing Integral with Gauss-Chebyshev Quadrature in MATLAB

[Fidelio]

Hello, anyone knows where y can find a program to compute the integral

∫ ( from -1 to 1) f(x)/ √(1-x^2) using the Gauss-Chebyshev quadrature, on matlab?

Thanks!

 

[AlephZero]

The formula for the integration points and weights is here: http://mathworld.wolfram.com/Chebyshev-GaussQuadrature.html

or in Abrimovitz and Stegun section 25.4.37 here: http://people.math.sfu.ca/~cbm/aands/page_889.htm

Some MATLAB code here (page 26): http://www.math.siu.edu/matlab/tutorial5.pdf

 

[Fidelio]

thanks so much AlephZero,

Could you check If it is correct ?

function int = chebquad(funct,accuracy)
f = inline(funct);
old_int = inf;
for n=1:1000

x = cos(((2*(1:n) - 1)/(2*n))*pi);
w = pi/n;
fx = f(x);
int = sum(w.*fx);
if abs(int_old-int) < abs(tol*int),
converge='y';
break;
end
old_int = int;
end

And now If I want to compute this integral \int_1^2 dx \frac { e^{2x} }{ ( (2-x) ( (1-x))^{1/2} } with an accuracy 10^-8 what could I do?