Mathematics

Problem

The area of the region between the curves

y = \sqrt{\frac{1 + \sin x}{\cos x}}

and

y = \sqrt{\frac{1 - \sin x}{\cos x}}

bounded by the line

x = 0

and

x = \frac{\pi}{4}

is :- [JEE 2008] (A)

\int_{0}^{\sqrt{2}-1} \frac{t}{(1+t^2)\sqrt{1-t^2}} dt

(B)

\int_{0}^{\sqrt{2}-1} \frac{4t}{(1+t^2)\sqrt{1-t^2}} dt

(C)

\int_{0}^{\sqrt{2}+1} \frac{4t}{(1+t^2)\sqrt{1-t^2}} dt

(D)

\int_{0}^{\sqrt{2}+1} \frac{t}{(1+t^2)\sqrt{1-t^2}} dt