# Double integral in polar coordinates

• January 16th 2010, 06:39 AM
cooltowns
Double integral in polar coordinates
Hi

I need help with the this following double integral. I know how to carry out double integrals but in this polar coordinates double integral case i am not sure of what limits to use.

Evaluate the double integral

$\iint_{D}ydA$ where $D$ is the region in the first quadrant that is outside the circle $r=2$and inside the cardioid $r=2(1+cos\theta)$.

any help is appreichated

(Happy)
• January 16th 2010, 06:59 AM
Calculus26
The region is symmetric about the x-axis and y is positive above and negative below so the integral will be 0.

See attachment
• January 16th 2010, 07:22 AM
cooltowns
its only to do with the first quadrant. So will the limits still be pi/2 and -pi/2 ?
and will the answer be 0 ?
• January 16th 2010, 07:24 AM
Calculus26
Missed the first quadrant part--- limits will be o to pi/2 and the answer will be 22/3 as in the attachment