as follows:
and that occurs at 
so they're going to be the limits of integration. To solve for the coordinates of the centroid 
, we need to solve for the area A first:![\displaystyle A = \int_a^b [f(x) - g(x)]dx](/tpl/images/1388/6358/228df.png)
![\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}[(x^2 + 1) - 6x^2]dx](/tpl/images/1388/6358/8ebc3.png)
is given by![\displaystyle \bar{x} = \dfrac{1}{A}\int_a^b x[f(x) - g(x)]dx](/tpl/images/1388/6358/a3b40.png)
is given by![\displaystyle \bar{y} = \frac{1}{A}\int_a^b \frac{1}{2}[f^2(x) - g^2(x)]dx](/tpl/images/1388/6358/27bb4.png)
![\:\:\:\:\:\:\:=\frac{75}{56} \left[-7x^5 + \frac{2}{3}x^3 + x \right]_{-\frac{1}{5}}^{+\frac{1}{5}}](/tpl/images/1388/6358/ea58f.png)
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