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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:
B
Let `" " f(x) = int e^(x) (x -1) (x - 2) dx `
`rArr " " f' (x) = e ^(x) (x - 1) (x -2)`

`therefore f ' (x) lt 0 ` for ` 1 lt x lt 2 `
`rArr f(x)` is decreasing for ` x in ( 1, 2)`.
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