1. The problem statement, all variables and given/known data ∫√(a2 - x2) dx 2. Relevant equations 3. The attempt at a solution What I've understood so far is its a substitution integral. Through the instruction of my lecture notes, I have ∫√(a2 - x2) dx Let u = sin-1(x/a) x = a*sin(u) dx = a*cos(u) This means that √(a2 - x2) = √(a2 - a2sin2(x)) Then as the trig identity of √(cos2(u) + sin2(u)) = 1. You can rearrange it to give cos(u) = √(1-sin2(u)) So √(a2 - a2sin2(u)) = √(a2 * cos2(u)) = a*cos(u) Now there is my problem, A lot of other sources say that rather than ∫a*cos(u) du it is ∫a2 * cos2(u) du and I don't understand why.