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The area of the region bonded by y=e^(x)...

The area of the region bonded by `y=e^(x),y=e^(-x),x=0` and x = 1 is (a) `e+(1)/(e)` (b) `log(4/e)` (c) `4log(4/e)` (d) `e+(1)/(e)-2`

A

`e+(1)/(e)`

B

`log(4//e)`

C

`4log(4//e)`

D

`e+(1)/(e)-2`

Text Solution

Verified by Experts

The correct Answer is:
D
The graph of the functions is as shown in the following figure :

`A=int_(0)^(1)(e^(x)-e^(-x))dx`
`=(e^(x)+e^(-x))_(0)^(1)`
`=(e+e^(-1))-(1+1)`
`=e+(1)/(e)-2`
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