Mathematics

# Integrate $\dfrac x{ \sqrt {1-x^2}}$ w.r.t $x$

##### SOLUTION
$\displaystyle \int \dfrac x {\sqrt {1-x^2}} dx$

Let $x=\cos t\implies dx =\sin tdt$

$\implies \displaystyle \int \dfrac {\cos t}{\sqrt {1-\cos ^2 t} }\sin t dt$

$\implies \displaystyle \int \cos t dt =-\sin t$

$=-\sin \cos ^{-1} x$

$=-\sin \sin ^{-1} \sqrt {1-x^2}$

$=-\sqrt {1-x^2}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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