5.4 Indefinite Integrals and the Net Change Theorem/25: Difference between revisions
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\begin{align} | \begin{align} | ||
\int_{-2}^{2}({3u+1})^2 du = \int | \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(2)^{3} + 3(2)^2 + 2] - [3(-2)^3 + 3(-2)^2 -2] \\[2ex] | |||
= | &= {52} \\[2ex] | ||
= {52} | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
Latest revision as of 19:40, 21 September 2022
![{\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(2)^{3}+3(2)^{2}+2]-[3(-2)^{3}+3(-2)^{2}-2]\\[2ex]&={52}\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/fa681af0f9f1a9c593756ef2a9ff9fba7ed449e9)