integrate ∫_0 ^(nπ) ϱ^((((8u)/(nπ)))) (1−cos2u)du


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Question Number 131452 by Engr_Jidda last updated on 04/Feb/21

$i n t e g r a t e$ $\int_{0}^{n π} ϱ^{(\frac{8 u}{n π})} (1 - c o s 2 u) d u$
	Answered by bramlexs22 last updated on 04/Feb/21

	$h i n t : l e t \frac{8 u}{n π} = t \Rightarrow 2 u = \frac{t n π}{4}; d u = \frac{n π}{8} d t$ $\begin{array}{cc} u = n π \Rightarrow t = 8 \\ u = 0 \Rightarrow t = 0 \end{array}$ $I = \int_{0}^{8} e^{t} (1 - \cos \frac{t n π}{4}) (\frac{n π}{8}) d t$ $u s i n g i n t e g r a t i o n b y p a r t s$
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