Originally Posted by

**circuscircus** I don't have an answer to check against but could someone let me know if I did this right?

**Formula for xbar:**

$\displaystyle x bar = \frac{My}{m}$

**Finding m:**

$\displaystyle m = p \int_{\sqrt{3}}^{0} \frac{1}{x^2+1}$

$\displaystyle m = p ( arctan(\sqrt{3}))$

**Finding My:**

$\displaystyle My = p \int_{0}^{\sqrt{3}} x * \frac{1}{x^2+1}$

$\displaystyle My = p \int_{0}^{\sqrt{3}} \frac{x}{x^2+1}$

$\displaystyle u=x^2+1$

$\displaystyle du=2x$

$\displaystyle = p * \frac{1}{2} \int_{1}^{4} 1/u$

$\displaystyle = p * \frac{1}{2} ( ln|4| - ln|1|) $

$\displaystyle = p * \frac{1}{2} ln|4/1|$

$\displaystyle = p * \frac{1}{2} ln|4|$

**x bar**

$\displaystyle x bar = \frac{ln|4|}{2arctan\sqrt{3}}$