i dont really get this prob....?

Question

http://i181.photobucket.com/albums/x85/ctti_3/untitled-76.jpg

Answer 1

Hi,
The problem is ∫(2-x)/(√(1-x²):
So, we separate this into the following:
2∫ dx/(√(1-x²) dx + ∫-xdx)/(√(1-x²)
= 2sin^(-1) x + (1/2) ∫(1-x²)^(-1/2)2(-xdx).... (The first term is of the form du√(a² -u²) where a = 1 and u = x. The integral of that is sin^(-1)(u/a) .)
= 2sin^(-1) x + (1-x²)^(1/2) +C ... (Use u^(n+1)/(n+1) for the second term.)
= 2sin-1 x +√ (1-x²) +C
This is a little tedious to do on this word processor, but I hope you can make it out okay.

FE