`int_(-(pi)/(4))^((pi)/(4)) (sin x - tan x ) dx` का मान क्या है ?

Options

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

Answer

C

Explanation

माना `l=int_(-pi//4)^(pi//4)(sin x-tan x)dx`
`f(x)=sin x -tan x`
`:.f(-x)=sin(-x)-tan(-x)`
`=-sin x+tanx " " [:'sin(-theta)-sin theta, tan(-theta)=-tan theta]`
`=-(sin x-tan x)`
`=-f(x)`
`:.f(x)` एक विषम फलन है ।
`:.l=int_(-pi//4)^(pi//4)(sin x-tan x)dx`
`=0" " [:'int_(-a)^(a)f(x)dx=0, " यदि" f(x) " एक विषम फलन हो " ]`