Find the [[../Area between Curves|Area between Curves]] $f(x)=12-x^2$ and $g(x)=x^2-6$ $\huge \begin{align} 12-x^2 &= x^2 -6 \\ 18&= 2x^2 \\ \sqrt 9 &= x \\ 3 &= x \\ \\ r^2 - 6 &= 0 \\ r &= \sqrt 6\\ \\ A &= \int_{0}^{3} \pa{12-x^2}\d x + \int_{\sqrt 6}^{3} \pa{x^2-6}\d x - \int_{0}^{\sqrt 6} \pa{x^2-6}\d x \\ &= \pa{ 12\cdot 3 - \frac{3^3}{3} } + \pa{ \frac{3^3}{3} -6\sqrt{3} + 6x - \frac{\sqrt{6}^3}{3} } - \frac{6^{\frac{3}{2}}}{3} +6\sqrt 6 \\&= 27 + \pa{ \frac{3^3}{3} -6\sqrt{3} + 6x - \frac{\sqrt{6}^3}{3} } - \frac{6^{\frac{3}{2}}}{3} +6\sqrt 6 \end{align}$