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The value of int(0)^(100) [ tan^(-1)x]dx...

The value of `int_(0)^(100) [ tan^(-1)x]dx` is

A

100

B

`100-tan^(-1)1`

C

100- tan 1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`underset(0)overset(100)int [ tan^(-1)x]dx=underset(0)overset(tan1)int [ tan^(-1)x]dx+underset(tan1)overset(100)int [ tan^(-1)x]dx`
`underset(0)overset(100)int [ tan^(-1)x]dx=underset(0)overset(tan1)int [ tan^(-1)x]0 dx+underset(0)overset(100)int1. dx =100- tan 1`
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