5.4 Indefinite Integrals and the Net Change Theorem/30: Difference between revisions
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\int_{1}^{2}\frac{y+5y^7}{y^3}dy &= \int_{1}^{2}\left(\frac{y}{y^3}+\frac{5y^7}{y^3}\right)dy = \int_{1}^{2}(y^{-2}+5y^{4})dy\\[2ex] | \int_{1}^{2}\frac{y+5y^7}{y^3}dy &= \int_{1}^{2}\left(\frac{y}{y^3}+\frac{5y^7}{y^3}\right)dy = \int_{1}^{2}(y^{-2}+5y^{4})dy\\[2ex] | ||
&= \frac{y^{-2+1}}{-2+1}+\frac{5y^{4+1}}{4+1}\bigg|_{1}^{2} | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 18:10, 26 August 2022
![{\displaystyle {\begin{aligned}\int _{1}^{2}{\frac {y+5y^{7}}{y^{3}}}dy&=\int _{1}^{2}\left({\frac {y}{y^{3}}}+{\frac {5y^{7}}{y^{3}}}\right)dy=\int _{1}^{2}(y^{-2}+5y^{4})dy\\[2ex]&={\frac {y^{-2+1}}{-2+1}}+{\frac {5y^{4+1}}{4+1}}{\bigg |}_{1}^{2}\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/20a89c255c1a0244952d403ff5d023c8a8039a5a)