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Ifinta^b(f(x))/(f(x)+f(a+b-x))dx=10 ,t h...

`Ifint_a^b(f(x))/(f(x)+f(a+b-x))dx=10 ,t h e n` (a) `b=22 ,a=2` (b) `b=15 ,1=-5` `b=10 ,a=-10` (d) `b=10 ,a=-2`

A

`b=22, a=2`

B

`b=15,a=-5`

C

`b=10, a=-10`

D

`b=10, a=-2`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Let `I=int_(a)^(b)(f(x))/(f(x)+f(a+b-x))dx`
`=int_(a)^(b)(f(a+b-x))/(f(a+b-x)+f(x))dx`
Adding 1 and 2 we get
`2I=int_(a)^(b)1dx=b-a`
or `I=((b-a)/2)=10` (given)
`:.b-a=20`
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