Center of mass question

[Trenters4325]

Find the center of mass of a region inside the circle x^2 + y^2 = 2x and outside the circle x^2 + y^2 = 1 with a density function of (x^2 + y^2)^(-1/2).

Change it to polar.

The back of my book says the mass is 2(sqrt(3) - pi/3)), but I think it is wrong.

 

[stapel]

Why do you think the book's answer is wrong? What were your steps and your answer?

Please be specific. Thank you.

Eliz.

 

[Trenters4325]

For the mass, I got \(\displaystyle \int\limits_{ - \pi /3}^{\pi /3} {\int\limits_1^{2\cos (\theta )} {r^2 drd\theta = \frac{{2\left( {9\sqrt 3 - \pi } \right)}}{9}} } = 2.766\)