7.1 Integration By Parts/30: Difference between revisions
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r^{2} &= u-4 \\[2ex] | r^{2} &= u-4 \\[2ex] | ||
2r\cdot dr &= du | 2r\cdot dr &= du \\[2ex] | ||
du &= \frac{1}{\sqrt{1-x^2}}\ \\[2ex] | du &= \frac{1}{\sqrt{1-x^2}}\ \\[2ex] | ||
Revision as of 11:54, 29 November 2022
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \int_{0}^{1}\frac{r^{3}}{\sqrt{4+r^{2}}}\cdot dr }
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}u&=4+r^{2}\\[2ex]r^{2}&=u-4\\[2ex]2r\cdot dr&=du\\[2ex]du&={\frac {1}{\sqrt {1-x^{2}}}}\ \\[2ex]\end{aligned}}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \int_{0}^{1}\frac{r^{3}}{\sqrt{4+r^{2}}}\cdot dr ~~~ = ~~~ \int_{0}^{1}r^{3}\cdot \frac{1}{\sqrt{4+r^{2}}}\cdot dr }