7.1 Integration By Parts/35

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_\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{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} & \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} }