7.1 Integration By Parts/53: Difference between revisions
No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
<math>y= xe^{-0.4x} ~~~ | <math>y= xe^{-0.4x} ~~~ y=0,x=5</math> | ||
<math> | <math> | ||
| Line 19: | Line 19: | ||
<math> | <math> | ||
\left [ \frac{5}{2}e^{-0.4x} \right ]\bigg|_{0}^{ | \left [ \frac{5}{2}e^{-0.4x} \right ]\bigg|_{0}^{5}+\int_{5}^{0}\frac{5}{2}e^{-0.4x}dx | ||
</math> | </math> | ||
Revision as of 16:38, 13 December 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 y= xe^{-0.4x} ~~~ y=0,x=5}
![{\displaystyle {\begin{aligned}\underbrace {\int _{0}^{5}xe^{-0.4x}dx} _{\begin{aligned}u&=x&dv&=e^{-0.4x}dx\\[0.6ex]du&=dx&v&={\frac {5}{2}}e^{-0.4x}\end{aligned}}\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/91d4a6c6285a2e1341ff3df89604c6777da55fd6)
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 \left [ \frac{5}{2}e^{-0.4x} \right ]\bigg|_{0}^{5}+\int_{5}^{0}\frac{5}{2}e^{-0.4x}dx }
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 &= -0.4x \\[2ex] du &= -0.4dx \\[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 \left (-\frac{25}{2}e^{-2}-0 \right )+\frac{5}{4}\int_{5}^{0}e^{u} }
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 -\frac{25}{2}e^{-2}+\left [ \frac{5}{4}\left ( e^{-0.4x} \right ) \right ]~~~=~~~ -\frac{25}{2}e^{-2}-\frac{25}{4}e^{-2}+\frac{25}{4}~~~=~~~ -\frac{75}{4}e^{-2}+ \frac{25}{4} }