6.1 Areas Between Curves/5: Difference between revisions
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\int_{-1}^{2}[(9-x^{2}) - (x+1)] dx | \int_{-1}^{2}[(9-x^{2}) - (x+1)] dx | ||
&= [9x-\frac{x^{3}}{3}-\frac{x^{2}}{2}-x]\Bigg|_{-1}^{2} = [9(2)-\frac{(2)^{3}}{3}-\frac{(2)^{2}}{2}-(2)-(9(-1)-\frac{(-1)^{3}}{3}-\frac{(-1)^{2}}{2}-(-1))] | &= [9x-\frac{x^{3}}{3}-\frac{x^{2}}{2}-x]\Bigg|_{-1}^{2} = [9(2)-\frac{(2)^{3}}{3}-\frac{(2)^{2}}{2}-(2)-(9(-1)-\frac{(-1)^{3}}{3}-\frac{(-1)^{2}}{2}-(-1))] | ||
Revision as of 19:12, 22 September 2022
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}&\color {red}\mathbf {y=x+1} &\color {royalblue}\mathbf {y=9-x^{2}} \\&x=-1&x=2\\\end{aligned}}}
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}[(9-x^{2}) - (x+1)] dx &= [9x-\frac{x^{3}}{3}-\frac{x^{2}}{2}-x]\Bigg|_{-1}^{2} = [9(2)-\frac{(2)^{3}}{3}-\frac{(2)^{2}}{2}-(2)-(9(-1)-\frac{(-1)^{3}}{3}-\frac{(-1)^{2}}{2}-(-1))] &= 18-\frac{8}{3}--2-2+9-\frac{1}{3}+\frac{1}{2}-1 = 19.5 \end{align} }