Question

Let the function $f: R \rightarrow R$ and $g: R \rightarrow R$ be defined by
$f(x)=e^{x-1}-e^{-|x-1|}$ and $g(x)=\frac{1}{2}\left(e^{x-1}+e^{1-x}\right)$.
Then the area of the region in the first quadrant bounded by the curves $y=f(x), y=g(x)$ and $x=0$ is

• A. $(2-\sqrt{3})+\frac{1}{2}\left(e-e^{-1}\right)$
• B. $(2+\sqrt{3})+\frac{1}{2}\left(e-e^{-1}\right)$
• C. $(2-\sqrt{3})+\frac{1}{2}\left(e+e^{-1}\right)$
• D. $(2+\sqrt{3})+\frac{1}{2}\left(e+e^{-1}\right)$

Answer 1

Answer: (A)

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

Answer 2

The Correct Option is (A): $(2-\sqrt{3})+\frac{1}{2}\left(e-e^{-1}\right)$