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A value of alpha such that int(a...

A value of `alpha` such that
`int_(alpha)^(alpha+1) (dx)/((x+a)(x+alpha+1))="loge"((8)/(8))` is

A

2

B

`-1/2`

C

`1/2`

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
D
`int_(alpha)^(alpha+1)(dx)/((x+alpha)(x+alpha+1))=int_(alpha)^(alpha+1)(1/((x+alpha))-1/((x+alpha+1)))`
`=In((x+alpha)/(x+alpha+1))]_(alpha)^(alpha+1)=In((2alpha+1)/(2 alpha+2))-In((2alpha)/(2 alpha+1))=In(((2alpha+1)^(2))/(2(alpha)(alpha+1)))=In 9/8 impliesalpha =-2`
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