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int0^1(dx)/(1+x+x^2)...

`int_0^1(dx)/(1+x+x^2)`

A

`(pi)/(sqrt(3))`

B

`(pi)/(3)`

C

`(pi)/(3sqrt(3))`

D

none of these

Text Solution

Verified by Experts

`I=int_(0)^(1)(dx)/({(x^(2)+x+(1)/(4))+(3)/(4)})=int_(0)^(1)(dx)/({(x+(1)/(2))^(2)+((sqrt(3))/(2))^(2)})=[(2)/(sqrt(3))tan^(-1).((x+(1)/(2)))/(((sqrt(3))/(2)))]_(0)^(1)=(pi)/(3sqrt(3))`
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