# Determining when an integral converges or diverges

1. Jul 10, 2009

### genu

1. The problem statement, all variables and given/known data
determine whether the integral converges or diverges:
$$\int_0^1\!\sqrt{\frac{(1+x)}{(1-x)}}dx$$

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?

2. Jul 10, 2009

### Dick

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.