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> | <math> | ||
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\begin{aligned} | \begin{aligned} | ||
u &= x & dv &= e^{-0.4x} dx \\[0.6ex] | u &= x & dv &= e^{-0.4x} dx \\[0.6ex] | ||
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</math> | </math> | ||
<math> | <math> | ||
\left [ \frac{5}{2}e^{-0.4x} \right ]+\int_{ | \left [ \frac{5}{2}e^{-0.4x} \right ]_{0}^{5}+\int_{0}^{5}\frac{5}{2}e^{-0.4x}dx | ||
</math> | </math> | ||
<math> | <math> | ||
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u &= -0.4x | u &= -0.4x | ||
\\[2ex] | \\[2ex] | ||
du &= | du &= -0.4dx \\[2ex] | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
<math> | <math> | ||
\left (-\frac{25}{2}e^{-2}-0 \right )+\frac{ | \left (-\frac{25}{2}e^{-2}-0 \right )+\frac{25}{4}\int_{0}^{5}e^{u} | ||
</math> | </math> | ||
<math> | <math> | ||
-\frac{25}{2}e^{-2}+\left [ \frac{ | -\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> | </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 \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} }