Question

The value of `int0 1tan^(-1)((2x-1)/(1+x-x^2))dx` is (A) 1 (B) 0 (C) -1 (D) `pi/4`
A. 1
B. 0
C. `-1`
D. None of these

Answer 1

Correct Answer - B
Let `I=underset(0)overset(1)int tan^(-1)((2x-1)/(1+x-x^(2)))dx`
`=underset(0)overset(1)int tan^(-1)((x+x-1)/(1-x(x-1)))dx`
`=underset(0)overset(1)int tan^(-1)dx+underset(0)overset(1)int tan^(-1)(x-1)dx`
`=underset(0)overset(1)int tan^(-1)dx+underset(0)overset(1)int tan^(-1)(1-x-1)dx`
`=underset(0)overset(1)int tan^(-1)dx+underset(0)overset(1)int tan^(-1)dx=0`