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If rArr int(0)^(1) (e^(-t))/(t+1) dt =a,...

If `rArr int_(0)^(1) (e^(-t))/(t+1) dt =a, "then"int_(b-1)^(b) (e^(-1))/(t-b-1)dt` is equal to

A

`ae^(-b)`

B

`-ae^(-b)`

C

`be^(b)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let t `=-u +b`. Then,
`rArr underset(0)overset(b)int (e^(-t))/(t-b-1) dt =underset(1)overset(0)int(e^(u-b))/(-u-1)(-du)`
`rArr underset(b-1)overset(b)int (e^(-t))/(t-b-1) dt =-underset(0)overset(1)int(e^(u-b))/(u+1)(-du)-e^(-b)underset(0)overset(1)intdu=ae^(-b)`
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