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• 17:53, 13 December 2022 Cynthiac61995@students.laalliance.org talk contribs created page 7.1 Integration By Parts/25 (Created page with "<math> \int_{0}^{1}\frac{y}{e^{2y}}dy u=y, -du=dy, dv=\frac{dy}{e^{2}y} &=e^{-2y}dy, v=\frac{-1}{2}e^{-2y} </math> <math> \begin{align} \int_{0}^{1}\frac{y}{e^{2y}}dy &=\left[\frac{-1}{2}ye^{-2y}\right]\bigg|_{0}^{1} + \frac{1}{2}\int_{0}{1}e^{-2y}dy \\[2ex] &= \left(\frac{-1}{2}e^{-2}+0\right)-\frac{1}{4}\left[e^{-2y}\right]\bigg|_{0}^(1) \\[2ex] &= \frac{-1}{2}e^{-2}-\frac{1}{4}e^{-2}+\frac{1}{4} \\[2ex] &= \frac{1}{4}-\frac{3}{4}e^{-2} \\[2ex] \end{align} </math>")