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### Section 2-3 : Center Of Mass

Find the center of mass for each of the following regions.

1. The region bounded by $$y = {x^3}$$ , $$x = - 2$$ and the $$x$$-axis.
2. The triangle with vertices $$(-2, -2)$$, $$(4, -2)$$ and $$(4,4)$$.
3. The region bounded by $$y = {\left( {x - 2} \right)^2}$$ and $$y = 4$$.
4. The region bounded by $$y = \cos \left( x \right)$$ and the x-axis between $$\displaystyle - \frac{\pi }{2} \le x \le \frac{\pi }{2}$$.
5. The region bounded by $$y = {x^2}$$ and $$y = 6 - x$$.
6. The region bounded by $$y = {{\bf{e}}^{2x}}$$ and the x-axis between $$- 1 \le x \le 1$$.
7. The region bounded by $$y = {{\bf{e}}^{2x}}$$ and $$y = - \cos \left( {\pi x} \right)$$ between $$\displaystyle - \frac{1}{2} \le x \le \frac{1}{2}$$.