Find polar moment of region inside circle r = 3 and outside cardiod r = 2 + sin 0

[VinnyCee]

Here is the problem:

Find the polar moment of the region that lies inside the circle r = 3 and outside the cardiod r = 2 + \sin\theta. Assume \delta = r\theta

Here is what I have:

I_{0} = I_{x} + I_{y}

I_{0} = \int_{0}^{2\pi}\int_{2 + \sin\theta}^{3}\;r^3\;\theta\;\sin^2\theta\;dr\;d\ theta + \int_{0}^{2\pi}\int_{2 + \sin\theta}^{3}\;r^3\;\theta\;\cos^2\theta\;dr\;d\ theta

I_{0} = \int_{0}^{2\pi}\int_{2 + \sin\theta}^{3}\;r^3\;\theta\;dr\;d\theta

Is this the correct setup? I don't have to manually evaluate this one, I just need to setup the integral limits and the integrand. Thank you in advance!

[dextercioby]

It looks okay to me...The cardioide & the circle have only one common point (y=3)

Daniel.