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## Homework Statement

Find the mass and center of mass of the region bounded by the cardioid r =

1 + cos(θ), assuming the density function is given by ρ = r.

## The Attempt at a Solution

The first part is simple enough, I set up the integral

[itex]\int_{0}^{2\pi}[/itex][itex]\int_{0}^{1+cos(\theta)}r dr d(\theta)[/itex]

I find the mass is 3pi/2

Now for the centre of, how do I set up the integrals? I know it would be the double integral of xρ drdθ, and then yρ drdθ, but do I keep the same limits? x would be rcos(θ) and y is rsin(θ), but this gives me some really weird functions to integrate.

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