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If I= underset(1)overset(2)(int)log(11)(...

If `I= underset(1)overset(2)(int)log_(11)(x^3 - x^2 + 6x -5)` dx, then:

A. `0 lt I lt 1/2`
B. `-1ltIlt1/2`
C. `-1ltIlt0`
D. `0lt Ilt 1`

A

`0 lt I lt (1)/(2)`

B

`-1 lt I lt (1)/(2)`

C

`-1 lt I lt 0`

D

`0 lt I lt 1`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x) = log_(11) (x^3 - x^2 + 6x - 5)`
`therefore f(X)` is increasing in (1,2) therefore `0 lt f(x) lt 1`
`0 lt I lt 1`
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