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

The value of `int_0^1tan^(-1)((2x-1)/(1+x-x^2))dx ,\ ` is
a.`1`
b. `-1`
c. `0`
d. `pi//4`

Text Solution

Verified by Experts

`I=int_0^1 tan^(-1)((2x-1)/(1+x-x^2))dx`
`I=int_0^1 tan^(-1)((x-(1-x))/(1+x(1-x)))dx`
`I=int_0^1 tan^(-1)x-tan^(-1)(1-x)dx -(1)`
`I=int_0^1 tan^(-1)(1-x)-tan^(-1)(1-(1-x))dx`
`I=int_0^1 tan^(-1)(1-x)-tan^(-1)x dx -(2)`
addind (1) and(2) we get,
2I=0
I=0
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