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The value of int(e^(-1))^(e) (dt)/(t(t...

The value of ` int_(e^(-1))^(e) (dt)/(t(t+1))` is equal to

A

1

B

` log(e/(1+e))`

C

` log(1/(1+e))`

D

` log (1+e)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `l=int_(e^(-1))^(e)(dt)/(t(t+1))`
`=int_(e^(-1))^(e)(1)/(t)dt-int_(e^(-1))^(e)(1)/((t+1))dt=[logt-log(t+1)]_(e^(-1))^(e)`
`=[loge-log(e-1)]=[loge^(-1)-log(e^(-1)+1)]`
`=log((e)/(e+1))-[-loge-log(e^(-1)+1)]`
`=log((e)/(e+1))+[loge((1)/(e)+1)]`
`=log_(e)e=1`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
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  10. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

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