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Let p(x) be a function defined on R such...



Let `p(x)` be a function defined on `R` such that `p'(x)=p'(1-x)` for all `x epsilon[0,1],p(0)=1` and `p(1)=41`.
Then `int_(0)^(1)p(x)dx` is equals to (a)`42` (b)`sqrt(41)` (c)`21` (d)`41`

A

`42`

B

`sqrt(41)`

C

`21`

D

`41`

Text Solution

Verified by Experts

The correct Answer is:
C
`p'(x)=p'(1-x)`
`impliesp(x)=-p(1-x)+c`
At `x=0`
`p(0)=-p(1)+cimplies42=c`
`:.p(x)=-p(1-x)+42`
`impliesp(x)+p(1-x)=42`
`I=int_(0)^(1)p(x)dx=int_(0)^(1)p(1-x)dx`
`:. 2I=int_(0)^(1)(p(x)+p(1-x))dx=int_(0)^(1)(42)dx`
`impliesI=21`
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