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The value of int0^1(x^4(1-x)^4)/(1+x^2)d...

The value of `int_0^1(x^4(1-x)^4)/(1+x^2)dxi s//a r e` `(22)/7-pi` (b) `2/(105)` `0` (d) `(71)/(15)-(3pi)/2`

A

`22/7-pi`

B

`2/105`

C

`0`

D

`71/15-(3pi)/2`

Text Solution

Verified by Experts

The correct Answer is:
A
`int_(0)^(1)(x^(6)-4x^(5)+5x^(4)-4x^(2)+4-4/(1+x^(2)))dx`
`=[(x^(7))/7-(2x^(6))/3+x^(5)-(4x^(3))/3+4x]_(0)^(1)-pi`
`=1/7-2/3+1-4/3+4-pi=22/7-pi`
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