The value of $\int_{0}^{\frac{\pi}{2}}\frac{\cos heta}{\sqrt{4 - \sin^{2} heta}}\ d heta$ is

Question

The value of $\int_{0}^{\frac{\pi}{2}}\frac{\cos	heta}{\sqrt{4 - \sin^{2}	heta}}\ d	heta$ is

Dr. Abubacker · Accepted Answer

(b)
Let $I = \int_{0}^{\pi/2}{\frac{\cos	heta}{\sqrt{4 - \sin^{2}	heta}}d	heta}$
Put $\sin{	heta = t\  \Rightarrow \ \cos{	heta d	heta = dt}}$
$	herefore\ I = \int_{0}^{1}\frac{dt}{\sqrt{4 - t^{2}}}$
$= \left\lbrack \sin^{- 1}\frac{t}{2} ightbrack_{0}^{1}$
$= \sin^{- 1}{\frac{1}{2} = \frac{\pi}{6}}$

Q. The value of $\int_{0}^{\frac{\pi}{2}}\frac{\cos\theta}{\sqrt{4 - \sin^{2}\theta}}\ d\theta$ is

Explanation

Reviewed by Dr. Abubacker

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