Mathematics

# Solve $\displaystyle \int\sqrt{\dfrac{a-x}{a+x}}dx$

##### SOLUTION
$= \displaystyle\int \dfrac{a-x}{\sqrt{a^2-x^2}}dx$

$= \displaystyle\int \dfrac{a}{\sqrt{a^2-x^2}}dx - \int \dfrac{1}{2}\dfrac{2x}{\sqrt{a^2-x^2}}dx$

$let a^2 - x^2 = t$
$-2x = dt$

$= a\displaystyle\int \dfrac{1}{\sqrt{a^2-x^2}}dx + \int \dfrac{1}{2}\dfrac{dt}{\sqrt{t}}$

$= a\sin^{-1}\dfrac{x}{a}+\dfrac{1}{2}*\dfrac{2}{1}t^{(\dfrac{1}{2})}$

$= a\sin^{-1}\dfrac{x}{a}+(a^2-x^2)^{(\dfrac{1}{2})}$ + $C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

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