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
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