7.1 Integration By Parts/53: Difference between revisions
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<math>y= xe^{-0.4x} ~~~ | <math>y= xe^{-0.4x} ~~~ y=0,x=5</math> | ||
<math>\int_{0}^{5}xe^{-0.4x}dx -\ | <math> | ||
\begin{align} | |||
\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{align} | |||
</math> | |||
<math> | |||
\left [ \frac{5}{2}e^{-0.4x} \right ]_{0}^{5}+\int_{0}^{5}\frac{5}{2}e^{-0.4x}dx | |||
</math> | |||
<math> | |||
\begin{align} | |||
u &= -0.4x | |||
\\[2ex] | |||
du &= -0.4dx \\[2ex] | |||
\end{align} | |||
</math> | |||
<math> | |||
\left (-\frac{25}{2}e^{-2}-0 \right )+\frac{25}{4}\int_{0}^{5}e^{u} | |||
</math> | |||
<math> | |||
-\frac{25}{2}e^{-2}+\left [ \frac{25}{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} | |||
</math> | |||
Latest revision as of 16:48, 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}
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} \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{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{5}{2}e^{-0.4x} \right ]_{0}^{5}+\int_{0}^{5}\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{25}{4}\int_{0}^{5}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{25}{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} }