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The area of the region bounded by the cu...

The area of the region bounded by the curve `y=e^x` and lines `x=0a n dy=e` is `e-1` (b) `int_1^e1n(e+1-y)dy` `e-int_0^1e^x dx` (d) `int_1^e1nydy`

A

`e-1`

B

`overset(e)underset(1)int" In "(e+1-y)dy`

C

`e-overset(1)underset(0)inte^(x)dx`

D

`overset(e)underset(1)int" In y "dy`

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
`"Required area "=overset(e)underset(1)int" In "y dy`
`=(y" In "y-y)_(1)^(e)`
`=(e-e)-{-1}`
`=1`
Also,
`overset(e)underset(1)int" In "yd y overset(e)underset(1)int" In "(e+1-y) dy`
`"Further Required area "=exx1-overset(1)underset(0)inte^(x)dx`
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