|Jul10-09, 01:41 PM||#1|
Determining when an integral converges or diverges
1. The problem statement, all variables and given/known data
determine whether the integral converges or diverges:
2. Relevant equations
I know what if the value is a finite number, it converges, otherwise it diverges. Teacher was was able to determine the fact just by looking at it... what is the procedure for this?
|Jul10-09, 02:02 PM||#2|
You look near the point where the integrand is singular, in this case near x=1. The numerator is ~2 and the denominator (1-x)=y is near zero. So the integral is going to have the same convergence properties as the integral of 1/sqrt(y) around zero. It converges.
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