# Homework Help: Comparison Test for improper integral

1. Nov 16, 2015

### sanhuy

1. The problem statement, all variables and given/known data
use the comparison theorem to determine whether ∫ 0→1 (e^-x/√x) dx converges.

2. Relevant equations
I used ∫ 0 → 1 (1/√x) dx to compare with the integral above

3. The attempt at a solution
i found that ∫ 0 → 1 (1/√x) dx = 2 ( by substituting 0 for t and take the limit of the defenite integral as t → 0^+) thus it is convergent. and (1/√x) > (e^-x/√x) so ∫ 0→1 (e^-x/√x) dx also converges.

But in my text book they only use the comparison theorem for the limits of integration from 0 to ∞. would it still be acceptable to use the comparison theorem for this problem for limits of integration from 0 to 1.
I don't see any particular reason why the comparison theorem for integrals wouldn't be valid with other limits of integration than $0$ to $\infty$.