7.1 Integration By Parts/30: Difference between revisions
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<math> \int_{0}^{1}\frac{r^{3}}{\sqrt{4+r^{2}}}\cdot dr ~~~ = ~~~ \int_{0}^{1}\frac{r}{2\sqrt{u}}\cdot dr </math> | <math> \int_{0}^{1}\frac{r^{3}}{\sqrt{4+r^{2}}}\cdot dr ~~~ = ~~~ \int_{0}^{1}\frac{r}{2\sqrt{u}}\cdot dr ~~~ = ~~~ \int_{0}^{1}\frac{u-4}{2\sqrt{u}}\cdot dr </math> | ||
Revision as of 11:59, 29 November 2022
![{\displaystyle {\begin{aligned}u&=4+r^{2}\\[2ex]r^{2}&=u-4\\[2ex]2r\cdot dr&=du\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/52ab8b5de0b47d5a125b84a3af2c6619c3c4367b)
