Question

The value of definite integral $\underset{0}{\overset{1}{\int }}\frac{dx}{\sqrt{1-x^2}\left(1+\sqrt{1-x^2}\right)}$ is equal to

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (A)

Put $x=\sin \theta$
$\therefore I=\underset{0}{\overset{\pi /2}{\int }}\frac{d\theta }{1+\cos \theta }={\left[\tan \frac{\theta }{2}\right]}_0^{\pi /2}=1$