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The value of underset(0)overset(1)int ta...

The value of `underset(0)overset(1)int tan^(-1) ((2x-1)/(1+x-x^(2)))dx` is

A

1

B

0

C

`-1`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let `= int_(0)^(1)tan^(-1)((2x-1)/(1+x-x^(2)))dx`
`=int_(0)^(1)tan^(-1)x dx+int_(0)^(1)tan^(-1)(x-1)dx`
`= int_(0)^(1)tan^(-1)x dx+int_(0)^(1)tan^(-1)(1-x-1)dx`
`= int_(0)^(1)tan^(-1)x dx - int_(0)^(1)tan^(-1)x dx =0`
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