What is the value of `int_((-pi)/(4))^(pi/4) (sin xx tan x) dx` ?

Options

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

Answer

C

Explanation

`int_((-pi)/(4))^(pi/4) (sinx - tanx) dx`.
Let `f(x) = sin x - tanx `
`f(-x) = sin(-x) - tan(-x)`
`= - sinx +tan x = - (sinx - tanx)`
`= -f(x)`.
So, `f(x)` is an odd function.
We know `int_(-a)^(a) f(x).dx = 0`, if `f(x)` is odd function.