# Thread: Double integral in polar coordinates

1. ## 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

2. The region is symmetric about the x-axis and y is positive above and negative below so the integral will be 0.

See attachment

3. 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 ?

4. Missed the first quadrant part--- limits will be o to pi/2 and the answer will be 22/3 as in the attachment