Question

The area of the region bounded by the curve $y=e^x,y=e^{-x}$ and the straight line $x=1$ is

• A. $e+\frac{1}{e}$
• B. $e-\frac{1}{e}$
• C. $e+\frac{1}{e}-2$
• D. $e-\frac{1}{e}+2$

Answer 1

The correct option is C $e+\frac{1}{e}-2$

Required area:
$=\underset{0}{\overset{1}{\int }}(e^x-e^{-x})dx={[e^x+e^{-x}]}_0^1$
$=e+\frac{1}{e}-1-1=e+\frac{1}{e}-2$