{ x}{{4-² x}} - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

..... Miscellaneous Exercise .....
Integrate the functions in Exercises 229 to 252.

Question : 237 of 271

Marks: +1, -0

\frac{\cos x}{\sqrt{4-\sin^2 x}}

Solution:

Let

I=\int \frac{\cos x}{\sqrt{4-\sin^2 x}}dx

Let

\sin x = t

\Rightarrow \cos x dx = dt

\therefore I=\int\frac{dt}{\sqrt{4-t^2}}

=\sin^{-1}\left(\frac{t}{2}\right)+C

=\sin^{-1}\left(\frac{\sin x}{2}\right)+C

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