1. The problem statement, all variables and given/known data ∫ from 0 to 1 of 1/sqrt(4-x^2) dx I know from Wolfram Alpha that the answer should be π/6, and that the indefinite integral would be arcsin(x/2). I see the connection between this and the antiderivative of arcsin, I'm just not sure how to handle the 4 rather than the 1--which technique to use. 2. Relevant equations ∫ 1/sqrt(1-x^2)dx is arcsin x 3. The attempt at a solution Tried a few ways. 1st attempt was to rewrite as ∫ (4-x^2)^(-1/2)dx then reverse the power and chain rules to get sqrt(4-x^2)/2x from 0 to 1=sqrt(3)/2. Knew this was incorrect but trying to get my thoughts flowing. 2nd attempt was with integration by parts, with u=1/sqrt(4-x^2) and dv=dx...etc. This one ended up pretty ugly though, as vdu was worse than the original equation. 3rd attempt was with u-substitution; this one looked like it was going to work then took a bad turn. Let u=4-x^2, produces ∫ from 4 to 3 1/sqrt(u) --> -sqrt(u) from 4 to 3, then plugging back the 4-x^2 ended up undefined. I was thinking of partial fractions but the sqrt throws me off. I'm studying for a placement exam and this is a question from a past exam in the class. Thanks to everyone very much for your help!