Area of circle in polar coordinates

Homework Statement

r=2cos(theta) I want to find the area using polar integration.

Homework Equations

area=(1/2)r^2 from 0-pi

The Attempt at a Solution

When I plug everything in I get 2pi as the answer. I'm in multivariable calculus so this is very frustrating. What am I doing wrong, I don't know, but it's really really really really bugging me. I have an extra 2 somewhere and I don't know where.