# Thread: Need help solving this integral

1. ## Need help solving this integral

Hi!

The problem says:

A region R in the plane consists of those points (x,y) which satisfy the inequalities

1_<x^2+y^2<_4
0_<x
0_<y

And the intgral is
SSR (x^2+y^2-1)dA

(a screenshot of the problem is attached)

2. ## Re: Need help solving this integral

Convert to polar coordinates. This gives you $1\le r \le 2$ and $0 \le \theta \le \dfrac{\pi}{2}$.

$\displaystyle \int_0^{\tfrac{\pi}{2}} \int_1^2 (r^2-1)r{dr}{d\theta} = \int_0^{\tfrac{\pi}{2}}\dfrac{9}{4}{d\theta} = \dfrac{9\pi}{8}$

3. ## Re: Need help solving this integral

Hi.

Why is (r^2−1) multiplied by r?