6.1 Areas Between Curves/5

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} & \color{red}\mathbf{y=x+1} & \color{royalblue}\mathbf{y=9-x^{2}} \\ & x=-1 & x=2 \\ \end{align} }

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_{-1}^{2}\left(9-x^{2}-x+1\right) dx &= \left[9x-\frac{x^{3}}{3}-\frac{x^{2}}{2}-x\right]\Bigg|_{-1}^{2} \\[2ex] &= \left[9(2)-\frac{(2)^{3}}{3}-\frac{(2)^{2}}{2}-(2)\right]-\left[9(-1)-\frac{(-1)^{3}}{3}-\frac{(-1)^{2}}{2}-(-1)\right] \\[2ex] &= \left[18-\frac{8}{3}-2-2\right]-\left[-9+\frac{1}{3}+\frac{1}{2}+1\right] \\[2ex] &= \frac{117}{6} \\[2ex] \end{align} }