I was absent last friday when we went through it in class, so I'm completely lost when it comes to solving it. If anyone could explain how to do them I'd be extremely greatful. Thanks. 1. The problem statement, all variables and given/known data It said use the substitution x = a sin theta. 2. Relevant equations I'm not sure how to write this, but here it goes: The integral of (Top limit = 1; Bottom limit = 0) sqrt(2 - x^2) dx 3. The attempt at a solution I let x = sqrt(2) sin theta; so dx = sqrt(2) cos theta dtheta. Then I subbed what I know for x and dx into the original equation - The integral of: sqrt(2 - 2 sin^2 theta) sqrt(2) cos theta dtheta. Now I took out 2 from the equation, and put it ouside of the integral - So now i have - (2)Integral of: Sqrt(1 - sin^2 theta) cos theta dtheta And I know that cos^2A + sin^2A = 1; So I can put cos^2 Theta into my equation - Now I have - (2)Integral of: sqrt(cos^2 theta) cos theta dtheta. Removing squareroot, and mulitplying the cos thetas gives me - (2)Integral of: 1/2(1 + cos2theta) dtheta then... Integral of: (1 + cos2theta) dtheta. then integrating... [theta + sin2theta/2] And thats where I'm stuck, I probably did that completely wrong anyway. Thanks. P.S. You don't even have to answer this particular question, even if you could work through a similar kind so I could see what to do it'd be perfect. Thanks.