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Let f(x)=inte^x(x-1)(x-2)dxdot Then f d...

Let `f(x)=inte^x(x-1)(x-2)dxdot` Then `f` decreases in the interval `(-oo,-2)` (b) `-2,-1)` `(1,2)` (d) `(2,+oo)`

A

`(-oo,-2)`

B

`(-2,-1)`

C

`(1,2)`

D

`(2,oo)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given that,
`f(x)=inte^(x)(x-1)(x-2)dx`
On differentiating, we get
`f'(x)=e^(x)(x-1)(x-2)`
Since, f(x) is decreasing.
`:." "f'(x)lt0`
`impliese^(x)(x-1)(x-2)lt0`
`implies" "(x-1)(x-2)lt0`
`implies" "1ltxlt2`
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