A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{2}\]
C) \[\frac{1}{2}\]
D) \[\frac{\pi }{4}\]
Correct Answer: D
Solution :
\[\int_{0}^{1}{\frac{dx}{x+\sqrt{1-{{x}^{2}}}}=\int_{0}^{\pi /2}{\frac{\cos \theta \,d\theta }{\sin \theta +\cos \theta }}}\]\[=\frac{\pi }{4}\], (Put \[x=\sin \theta ,\,dx=\cos \theta \,d\theta \]).
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