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What int(0)^(2) (dx)/(x^(2) + 4) equal t...

What `int_(0)^(2) (dx)/(x^(2) + 4)` equal to ?

A

`pi/2`

B

`pi/4`

C

`pi/8`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
C
Let `I = int_(0)^(2)(dx)/(x^(2) + 4) = int_(0)^(2) (dx)/(x^(2) + (2)^(2))`
`= 1/2[tan^(-1)'x/2]_(0)^(-2) = 1/2[tan^(1)(1) - tan^(-1)(0)]`
`= 1/2[pi/4-0] = pi/8`
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NDA PREVIOUS YEARS-DEFINITE INTEGRATION & ITS APPLICATION-DIRECTIONS
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