7.1 Integration By Parts/19: Difference between revisions
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<math> | <math> | ||
\begin{align} | \begin{align} | ||
\int_{0}^{\pi} (t sin3t) dt\\[2ex] | |||
&= \int_{0}^{\pi} \frac{1}{2} t^{2} \frac{1}{2} sin3t^{2}\\[2ex] | &= \int_{0}^{\pi} \frac{1}{2} t^{2} \frac{1}{2} sin3t^{2}\\[2ex] | ||
&= \int_{0}^{\pi} \frac{1}{2} \pi^{2} \frac{1}{2} sin3\pi^{2}\\[2ex] | &= \int_{0}^{\pi} \frac{1}{2} \pi^{2} \frac{1}{2} sin3\pi^{2}\\[2ex] | ||
&= \frac{\pi}{3} | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
Latest revision as of 02:33, 16 December 2022
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\int _{0}^{\pi }(tsin3t)dt\\[2ex]&=\int _{0}^{\pi }{\frac {1}{2}}t^{2}{\frac {1}{2}}sin3t^{2}\\[2ex]&=\int _{0}^{\pi }{\frac {1}{2}}\pi ^{2}{\frac {1}{2}}sin3\pi ^{2}\\[2ex]&={\frac {\pi }{3}}\end{aligned}}}