What is the area bounded by the curves `y=e^x ,y =e ^-x` and the straight line `x=1` ?

Options

A. `e+(1)/(e)`
B. `e+(1)/(e)+2`
C. `e+(1)/(e)-2`
D. `e-(1)/(e)+2`

Answer

C

Explanation

Given curves are `y=e^(x)andy=e^(-x)`
The point of intersection is `e^(-x)=e^(x)`
implies x = 0 implies y = 1
So, the point of intersection is (0, 1).
`therefore` Area of bounded region ABC.
`=int_(0)^(1)(e^(x)-e^(-x))dx=[e^(x)+e^(-x)]_(0)^(1)`
`=[e^(1)+e^(-1)-(e^(0)+e^(-0))]=[e+(1)/(e)-(1+1)]=e+(1)/(e)-2`