JEE Advance - Mathematics (1988 - No. 8)
Evaluate $$\int\limits_0^1 {\log \left[ {\sqrt {1 - x} + \sqrt {1 + x} } \right]dx} $$
$$\frac{1}{2} \left[\log 2 + \frac{\pi}{4} - 1\right]$$
$$\log 2 + \frac{\pi}{2} - 1$$
$$\frac{1}{4} \left[\log 2 + \frac{\pi}{2} - 1\right]$$
$$\frac{1}{2} \left[\log 2 + \frac{\pi}{2} - 1\right]$$
$$\frac{1}{2} \left[\log 2 - \frac{\pi}{2} - 1\right]$$