7.1 Integration By Parts/35

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}&\int _{\sqrt {\frac {\pi }{2}}}^{\sqrt {\pi }}\ \theta ^{3}cos(\theta ^{2})d\theta &u=\theta ^{2}\\[2ex]&du=2\theta d\theta \\[2ex]&{\frac {1}{2}}du=\theta d\theta \end{aligned}}}

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} & \int{}^{} u\cdot cos(u) du & w=u \\[2ex] & wu=du & dv= cos(u) dx & v= sin(u) \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 \begin{align} & u\cdot sin(u) - \int{}^{} sin(u) du &= \frac{1}{2}u \cdot sin(u) + \frac{1}{2}cos(u)\bigg|_{\frac{\pi}{2}}^{\pi} &= \frac{1}{2}(\pi) \cdot sin(\pi) + \frac{1}{2} cos(\pi) - (\frac{1}{2}(\frac{\pi}{2}) \cdot sin(\frac{\pi}{2}) + \frac{1}{2} cos(\frac{\pi}{2})) \\[2ex] &= \frac{1}{2} (\pi)(0) + \frac{1}{2} (-1) - ( \frac{\pi}{4} + \frac{1}{2}(0) \\[2ex] &= -\frac{1}{2} - \frac{\pi}{4} \end{align} }