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The value of int0^1 (x^4+1)/(x^2+1)dx is...

The value of `int_0^1 (x^4+1)/(x^2+1)dx` is

A

`(1)/(6)(3pi-4)`

B

`(1)/(6)(3-4pi)`

C

`(1)/(6)(3pi+4)`

D

`(1)/(6)(3+4pi)`

Text Solution

Verified by Experts

The correct Answer is:
A
`int_(0)^(1)(x^(4)+1)/(x^(2)+1)dx=int_(0)^(1)(x^(4)-1)/(x^(2)+1)dx+2int_(0)^(1)(dx)/(1+x^(2))`
`int_(0)^(1)(x^(2)-1)dx+2int_(0)^(1)(dx)/(1+x^(2))`
`=[(x^(3))/(3)-x]_(0)^(1)+[2tan^(-1)x]_(0)^(1)`
`=-(2)/(3)+(pi)/(2)=(3pi-4)/(6)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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