Is it compulsory to use those test?. Take into account that:
so, we can expand by continuity the function taking hence, the integral is convergent.
Alternatively:
etc.
Hi,
I have to test the integral from 0 to pi of sin(x)/sqrt(pi-x) for convergence using the direct comparison test or the limit comparison test.
I know I can't integrate so I have to find a function that is either always greater than sin(x)/sqrt(pi-x) or do the limit comparison test on it.
I'm not quite sure how to approach this one.