How can I find the area under a polar curve with the equation r^2 = 4cos(2θ)?

[johnhuntsman]

r² = 4cos(2θ)

First I graph it. Then I set up the integral.

_____π
(1 / 2)∫ 4cos(2θ) dθ
_____0

________π
= [sin(2θ)]
________0

I thought the limits ought to be π and 0, but that comes out to zero. I pick other limits and they come out to 0. My graph matches the one in the back of the book. I know I've integrated correctly. I think the problem is the limits I'm picking somehow. The correct answer is 4.

[Edit] I also picked (π / 4) and -(π / 4) as limits, but that certainly didn't get me 4. [Edit]

 

[johnhuntsman]

Forget it I see what I'm doing. I'm only finding the area of one loop. My bad. Feel free to delete this post if you're a mod.