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

Answer

C

Explanation

Given equations of curces are `y = e^(x)` and `y =e^(-x)`
`rArr e^(x) = (1)/(e^(x)) rArr e^(2x) = e^(0) rArr x = 0`
`:.` Required area `= int_(0)^(1) (e^(x) - e^(-x))dx `
`= [e^(x) + e^(-x)]_(0)^(1) = e+e^(-1) - (e^(0)+e^(-0))`
`= (e+1/e - 2)` sq unit