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Let f be a positive function. Let I1=in...

Let `f` be a positive function. Let `I_1=int_(1-k)^k xf([x(1-x)]dx ,` `I_2=int_(1-k)^kf[x(1-x)]dx ,w h e r e2k-1> 0. T h e n(I_1)/(I_2)i s` 2 (b) `k` (c) `1/2` (d) 1

A

2

B

k

C

`1//2`

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
Given , `I_(1)=int_(1-k)^(k)xf[x(1-x)]dx`
`rArrI_(1)=int_(1-k)^(k)(1-x)f[(1-x)x]dx`
`=int_(1-k)^(k)f[(1-x)]dx]int_(1-k)^(k)xf(1-x)]dx`
`rArrI_(1)=I_(2)-I_(1)rArr(I_(1))/(I_(2))=(1)/(2)`
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