7.1 Integration By Parts/53: Difference between revisions
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\left [ \frac{5}{2}e^{-0.4x} \right ]+\int_{5}^{0}\frac{5}{2}e^{-0.4x}dx | \left [ \frac{5}{2}e^{-0.4x} \right ]\bigg|_{1}^{0}+\int_{5}^{0}\frac{5}{2}e^{-0.4x}dx | ||
</math> | </math> | ||
Revision as of 16:36, 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} ~~~ x=0,x=1}
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 ]\bigg|_{1}^{0}+\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} }