Question

integration of dx/a^2+x^2 limit from 0 to infinite​

Answer 1

$\begin{gathered}\Large{\bold{\pink{\underline{Formula \: Used \::}}}} \end{gathered}$

$\boxed{ \pink{:\implies \tt \: \int\: \dfrac{dx}{ {x}^{2} + {a}^{2} } dx = \dfrac{1}{a} {tan}^{ - 1} \dfrac{x}{a} + c}}$

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$\large\underline\purple{\bold{Solution :- }}$

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$:\implies \tt \: \int_0^ \infty \: \dfrac{dx}{ {x}^{2} + {a}^{2} } dx$

$:\implies \tt \: \dfrac{1}{a} \bigg [ {tan}^{ - 1} \dfrac{x}{a} \bigg]_0^ \infty$

$:\implies \tt \: \dfrac{1}{a} ( {tan}^{ - 1} \infty \: - \: {tan}^{ - 1} 0)$

$:\implies \tt \: \dfrac{1}{a} \: (\dfrac{\pi}{2} - 0)$

$:\implies \tt \: \dfrac{\pi}{2a}$

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$\boxed {\pink{ :\implies \tt \: \int_0^ \infty \: \dfrac{dx}{ {x}^{2} + {a}^{2} } dx = \dfrac{\pi}{2a} }}$

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