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The value of integral I = int(0)^(pi//4)...

The value of integral `I = int_(0)^(pi//4) (tan^(2)x + 2sin^(2)x) dx` is:

A

2

B

0

C

`-(1)/(2)`

D

`(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
The value ……….
`I = overset(pi//4)underset(0)int (tan^(2)x+2sin^(2)x)dx`
`= overset(pi//4)underset(0)int (sec^(2)x - 1+1-cos2x)dx`
`= overset(pi//4)underset(0)int sec^(2)x dx - overset(pi//4)underset(0)int cos 2x dx`
`=|tan x|_(0)^(pi//4) - |(sin2x)/(2)|_(0)^(pi//4)`
`=(1-0) - ((1)/(2) - 0) = (1)/(2)`
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