7.1 Integration By Parts/7: Difference between revisions
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(Created page with "<math> \begin{align} &=\int x^2 sin (\pi x)\\[2ex] & U=x^2 , du= 2xdx , dv= sin(\pi x)dx , v=-\frac{1}{\pi}cos(\pi x) \\[2ex] &=-\frac{x^2}{\pi}cos(\pi x) +\frac{2}{\pi} \int x cos (\pi x) dx\\[2ex] &U=x, du= dx, dv= cos(\pi x) dx, v=\frac{1}{\pi}sin (\pi x) \\[2ex] &=-\frac{x^2}{\pi}cos(\pi x)+ \frac{2}{\pi}[\frac{x}{\pi}sin(\pi x) - \frac{1}{\pi}\int sin (\pi x) dx]\\[2ex] &= -\frac{x^2}{\pi}cos(\pi x)+ \frac{2}{\pi}[\frac{x}{\pi}sin(\pi x) - \frac{1}{\pi^2}cos(\pi x...") |
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&= -\frac{x^2}{\pi}cos(\pi x)+ \frac{2}{\pi}[\frac{x}{\pi}sin(\pi x) - \frac{1}{\pi^2}cos(\pi x) ] +c\\[2ex] | &= -\frac{x^2}{\pi}cos(\pi x)+ \frac{2}{\pi}[\frac{x}{\pi}sin(\pi x) - \frac{1}{\pi^2}cos(\pi x) ] +c\\[2ex] | ||
\end{align} | \end{align} | ||
< | </math> | ||
Revision as of 05:57, 29 November 2022
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}&=\int x^{2}sin(\pi x)\\[2ex]&U=x^{2},du=2xdx,dv=sin(\pi x)dx,v=-{\frac {1}{\pi }}cos(\pi x)\\[2ex]&=-{\frac {x^{2}}{\pi }}cos(\pi x)+{\frac {2}{\pi }}\int xcos(\pi x)dx\\[2ex]&U=x,du=dx,dv=cos(\pi x)dx,v={\frac {1}{\pi }}sin(\pi x)\\[2ex]&=-{\frac {x^{2}}{\pi }}cos(\pi x)+{\frac {2}{\pi }}[{\frac {x}{\pi }}sin(\pi x)-{\frac {1}{\pi }}\int sin(\pi x)dx]\\[2ex]&=-{\frac {x^{2}}{\pi }}cos(\pi x)+{\frac {2}{\pi }}[{\frac {x}{\pi }}sin(\pi x)-{\frac {1}{\pi ^{2}}}cos(\pi x)]+c\\[2ex]\end{aligned}}}