6.1 Areas Between Curves/5: Difference between revisions
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\int_{-1}^{2}[(9-x^{2}) - (x+1)] dx &= [(9x-\frac{x^{3}}{3}-\frac{x^{2}}{2}-x)]\Bigg|_{-1}^{2} \\[2ex] | \int_{-1}^{2}[(9-x^{2}) - (x+1)] dx &= [(9x-\frac{x^{3}}{3}-\frac{x^{2}}{2}-x)]\Bigg|_{-1}^{2} \\[2ex] | ||
&=[9(2)-\frac{(2)^{3}}{3}-\frac{(2)^{2}}{2}-(2)]-[(9(-1)-\frac{(-1)^{3}}{3}-\frac{(-1)^{2}}{2}-(-1))] \\[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] | ||
Revision as of 19:31, 22 September 2022
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 (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\int _{-1}^{2}[(9-x^{2})-(x+1)]dx&=[(9x-{\frac {x^{3}}{3}}-{\frac {x^{2}}{2}}-x)]{\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]&=[18-{\frac {8}{3}}-2-2]-[-9+{\frac {1}{3}}-{\frac {1}{2}}+1]\\[2ex]&={\frac {117}{6}}\\[2ex]\end{aligned}}}