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. Thanks for reading :).