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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 in [0,""1],""p(0)""=""1` and `p(1)""=""41` . Then `int_0^1p(x)dx` equals (1) 21 (2) 41 (3) 42 (4) `sqrt(41)`

A

`42`

B

`sqrt(41)`

C

`21`

D

`41`

Text Solution

AI Generated Solution

To solve the problem, we need to find the integral \( \int_0^1 p(x) \, dx \) given the conditions on the function \( p(x) \). ### Step-by-Step Solution: 1. **Given Conditions**: We have the derivative condition: \[ p'(x) = p'(1 - x) \quad \text{for all } x \in [0, 1] ...
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