Area of circle in polar coordinates

[Malabeh]

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.

 

[Malabeh]

EDIT: I don't know how to delete a post but I got it. My calculator was in degree mode.

 

[LCKurtz]

EDIT: I don't know how to delete a post but I got it. My calculator was in degree mode.

While you may have gotten the correct answer, if you plot that circle you will see that the appropriate interval of integration would be $[-\frac \pi 2,\frac \pi 2]$, not $[0,\pi]$.

 

[Malabeh]

While you may have gotten the correct answer, if you plot that circle you will see that the appropriate interval of integration would be $[-\frac \pi 2,\frac \pi 2]$, not $[0,\pi]$.

It works both ways, does it not?