6.1 Areas Between Curves/15

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

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

${\begin{aligned}\tan(x)&=2\sin(x)\\\tan(x)-2\sin(x)&=0\\x&=0\\\end{aligned}}$