Thread: 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

where is the region in the first quadrant that is outside the circle and inside the cardioid .

any help is appreichated

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

See attachment

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 ?

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