- #1

jojo13

- 20

- 1

## Homework Statement

Find the area of the region that consists of all points that lie

**within**the circle r = 1 but

**outside**the polar equation r = cos(2θ)

## Homework Equations

A = ∫ 1/2 (r2^2 - r1^2) dθ, where r2 is outer curve and r1 is inner curve.

## The Attempt at a Solution

Here is what the graph looks like if you want to see it: http://www.wolframalpha.com/input/?i=r+=+cos(2x)+polar

Ok so first I had to find out the limits for my integral. I set: 1 = cos(2θ) and got that θ = ∏.

Now I made my integral, but instead of going from -∏ to ∏ I went from 0 to ∏ and multiplied it by 2

A = 2 ∫ 1/2 [(1^2) - (cos(2θ)^2)] dθ, from 0 to ∏

A = ∫ [ (1) - (1/2 cos(4θ) +1)] dθ, from 0 to ∏

I solved it and received: ∏ - ∏/2

Which equals ∏/2.

Just want to know if I did it right. The main part I was worried about was the limits for my integral.