`int_(0)^(pi//4) e^(x) (tan x+ sec^(2)x) dx`

Options

A. 2
B. 0
C. `-(1)/(2)`
D. `(1)/(2)`

Answer

D

Explanation

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)`