` I= int _(0)^(pi//2) log ((4+3 sin x)/(4+3 cos x))dx ` का मान है

Options

A. 2
B. `(3)/(4)`
C. 0
D. `-2`

Answer

C

Explanation

माना कि ` I = int _(0)^(pi//2) log ((4+3 sin x)/(4+3 cos x))dx" "` …(1)
समाकल्य में x कि जगह `(pi/2-x)` रखने पर हमें मिलता है ,
` I = int _(0)^(pi//2) log ((4+3 sin (pi/2-x))/(4+3cos (pi/2 -x)))dx `
या , ` I = int _(0)^(pi//2) log ((4+3 cos x )/(4+3 sin x )) dx " " ` ... (2)
` (1) + (2) rArr 2I = int _(0)^(pi//2) log [ ((4+3 sin x)/(4+3sin x)) ((4+3 cos x)/(4+3 sin x ))] dx `
` = int _(0)^(pi//2) log 1 dx = 0 " " [ :' log 1 = 0 ] `
` :. I = 0 `