6.1 Areas Between Curves/18

${\begin{aligned}&\color {red}\mathbf {y=8-x^{2}} &\color {royalblue}\mathbf {y=x^{2}} \\&x=-3&x=3\\\end{aligned}}$

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

$x=\pm 2$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} \int_{-2}^{2} \left((8-x^2) - (x^2)\right)dx &= \int_{-2}^{2}\left(8-2x^2\right)dx \\[2ex] &= \left(8x-\frac{2x^3}{3}\right)\bigg|_{-2}^{2} \end{align} }