Mathematics

Problem

Let the functions

f: \mathbb{R} \to \mathbb{R}

and

g: \mathbb{R} \to \mathbb{R}

be defined by

f(x) = e^{x-1} - e^{-|x-1|}

and

g(x) = \frac{1}{2}(e^{x-1} + e^{1-x})

. Then the area of the region in the first quadrant bounded by the curves

y = f(x)

y = g(x)

and

x = 0

is: [JEE-Advanced 2020] (A)

(2 - \sqrt{3}) + \frac{1}{2}(e - e^{-1})

(B)

(2 + \sqrt{3}) + \frac{1}{2}(e - e^{-1})

(C)

(2 - \sqrt{3}) + \frac{1}{2}(e + e^{-1})

(D)

(2 + \sqrt{3}) + \frac{1}{2}(e + e^{-1})