6.1 Areas Between Curves/13

$\color {red}{y=12-x^{2}}$

$\color {blue}{y=x^{2}-6}$

$\int _{-3}^{3}\left|(12-x^{2})-(x^{2}-6)\right|dx$ ${\begin{aligned}12-x^{2}&=x^{2}-6\\18&=2x^{2}\\9&=x^{2}\\\pm 3&=x\end{aligned}}$

${\begin{aligned}\int _{-3}^{3}\left|(12-x^{2})-(x^{2}-6)\right|dx&=(12x-{\frac {1}{3}}x^{3})-({\frac {1}{3}}x^{3}-6x){\Bigg |}_{-3}^{3}\\&=36-(-36)\\&=72\end{aligned}}$