- #1

VinnyCee

- 489

- 0

**:**

__Here is the problem__Find the polar moment of the region that lies inside the circle [tex]r = 3[/tex] and outside the cardiod [tex]r = 2 + \sin\theta[/tex]. Assume [tex]\delta = r\theta[/tex]

**:**

__Here is what I have__[tex]I_{0} = I_{x} + I_{y}[/tex]

[tex]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[/tex]

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

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!