如何避免数值积分中的奇异性

Question

I want to numerically integrate the following with Matlab:

fun = @(t) (((1 - (-1)^n * cos(n*pi*t/R))) ./ t);
hn = integral(fun, 0, (sqrt(R^2 - x^2)));

For now, I just avoided to evaluate the integral in 0, are they any way to encounter the singularity at this point.

Answer 1

If you use eps instead of 0 as the lower limit in your integral , I guess then you can also make it

R=101; 
X=linspace(0,R,1001)';
for n=1:10 
    for c=1:length(X) 
        x=X(c); 
        fun=@(t) (((1 - (-1)^n*cos(n*pi*sqrt(t.^2+x.^2)/R)))./sqrt(t.^2+x.^2)); 
        hn(c,n) = integral(fun,eps,(sqrt(R^2-x^2))); 
    end
end