7.1 Integration By Parts/30: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| Line 14: | Line 14: | ||
</math> | </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 | <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 du ~~~ = ~~~ \frac{}{}\frac{1}{2} \int_{0}^{1} \left (\frac{u}{\sqrt{u}} - \frac{4}{\sqrt{u}} \right ) \cdot du </math> | ||
Revision as of 12:04, 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)
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \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 du~~~=~~~{\frac {}{}}{\frac {1}{2}}\int _{0}^{1}\left({\frac {u}{\sqrt {u}}}-{\frac {4}{\sqrt {u}}}\right)\cdot du}