5.4 Indefinite Integrals and the Net Change Theorem/29: Difference between revisions
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\int_{-2}^{-1}\left(4y^3+\frac{2}{y^3}\right)dy &= \int_{-2}^{-1}\left(4y^3+2y^{-3}\right)dy\\[2ex] | \int_{-2}^{-1}\left(4y^3+\frac{2}{y^3}\right)dy &= \int_{-2}^{-1}\left(4y^3+2y^{-3}\right)dy\\[2ex] | ||
&= \left[y^4-y^-2\right]_{-2}^{-1} \\[2ex] | &= \left[y^{4}-y^{-2}\right]_{-2}^{-1} \\[2ex] | ||
&= (1-1)-\left(16-\frac{1}{4}\right) \\[2ex] | &= (1-1)-\left(16-\frac{1}{4}\right) \\[2ex] | ||
&= \frac{ | &= -\frac{63}{4} | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Latest revision as of 19:40, 21 September 2022
![{\displaystyle {\begin{aligned}\int _{-2}^{-1}\left(4y^{3}+{\frac {2}{y^{3}}}\right)dy&=\int _{-2}^{-1}\left(4y^{3}+2y^{-3}\right)dy\\[2ex]&=\left[y^{4}-y^{-2}\right]_{-2}^{-1}\\[2ex]&=(1-1)-\left(16-{\frac {1}{4}}\right)\\[2ex]&=-{\frac {63}{4}}\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/9414bcb4e5607f5be5cdc4d4bc92be25a0964afe)