Mathematics

Integrate the function    $$\displaystyle \frac {\cos x}{\sqrt {4-\sin^2x}}$$


SOLUTION
Let $$\sin x=t\Rightarrow \cos x dx=dt$$
$$\displaystyle \Rightarrow \int \frac {\cos x}{\sqrt {4-\sin^2x}}dx=\int \frac {dt}{\sqrt {(2)^2-(t)^2}}$$
$$\displaystyle =\sin^{-1}\left (\frac {t}{2}\right )+C$$
$$\displaystyle =\sin^{-1}\left (\frac {\sin x}{2}\right )+C$$
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Subjective Medium Published on 17th 09, 2020
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