5.4 Indefinite Integrals and the Net Change Theorem/25: Difference between revisions
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\int_{-2}^{2}({3u+1})^2 du &= \int(9u^2+6u+1)du \\[2ex] | \int_{-2}^{2}({3u+1})^2 du &= \int(9u^2+6u+1)du \\[2ex] | ||
&= | &= \left(3u^3+3u^2+u\right)\bigg|_{-2}^{2} \\ [2ex] | ||
&= {3\cdot 2^3 + 3\cdot 2^2 +2 - 3\cdot -2^3 + 3 \cdot-2^2 -2} \\[2ex] | &= {3\cdot 2^3 + 3\cdot 2^2 +2 - 3\cdot -2^3 + 3 \cdot-2^2 -2} \\[2ex] | ||
&= {52} \\[2ex] | &= {52} \\[2ex] | ||
Revision as of 15:03, 21 September 2022
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\int _{-2}^{2}({3u+1})^{2}du&=\int (9u^{2}+6u+1)du\\[2ex]&=\left(3u^{3}+3u^{2}+u\right){\bigg |}_{-2}^{2}\\[2ex]&={3\cdot 2^{3}+3\cdot 2^{2}+2-3\cdot -2^{3}+3\cdot -2^{2}-2}\\[2ex]&={52}\\[2ex]\end{aligned}}}