6.1 Areas Between Curves/15

${\begin{aligned}&\color {red}\mathbf {y=\tan(x)} &\color {royalblue}\mathbf {y=2\sin(x)} \\&x=-3&x=3\\\end{aligned}}$

$\int _{-{\frac {\pi }{3}}}^{\frac {\pi }{3}}\left|(8-x^{2})-(x^{2})\right|dx$

${\begin{aligned}8-x^{2}&=x^{2}\\-2x^{2}&=-8\\x^{2}&=4\\x&=\pm 2\end{aligned}}$