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 </math> | <math> \int_{0}^{1}\frac{r^{3}}{\sqrt{4+r^{2}}}\cdot dr </math> | ||
<math> | <math> | ||
\begin{align} | \begin{align} | ||
u &= | u &= 4+r^{2}{x} | ||
\\[2ex] | \\[2ex] | ||
du &= \frac{1}{\sqrt{1-x^2}}\;dx \\[2ex] | du &= \frac{1}{\sqrt{1-x^2}}\;dx \\[2ex] | ||
| Line 12: | Line 10: | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
<math> \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 </math> | |||
Revision as of 11:46, 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 (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 \begin{align} u &= 4+r^{2}{x} \\[2ex] du &= \frac{1}{\sqrt{1-x^2}}\;dx \\[2ex] \end{align} }
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 }