Originally Posted by

**Jameson** What is the center of mass of the region bounded by $\displaystyle y=\sqrt{3}|x|$ and the line y=3?

A) (0,0)

B) (0,1)

c) (0,2)

d) (0,3)

Ok, I know the x-coordinate of the center of mass is 0 because this is an even function. The y-coordinate of the center of mass can be found by this correct? $\displaystyle \frac{\int\int_{R}xdydx}{\int\int_{R}dydx}$?

If so I first must find the bounds. I set $\displaystyle \sqrt{3}|x|=3$ and get that the two graphs intersect at +-$\displaystyle \frac{3}{\sqrt{3}}$ or $\displaystyle \sqrt{3}$

So if this correct then the y-coordinate of the center of mass is $\displaystyle \frac{\int_{-\sqrt{3}}^{\sqrt{3}}\int_{\sqrt{3}|x|}^{3}xdydx}{\ int_{-\sqrt{3}}^{\sqrt{3}}\int_{\sqrt{3}|x|}^{3}dydx}$

I hope someone can check me up to here. Thanks.