∫-(π)/2(π)/2log⁡(2-sin⁡ x)/(2+sin⁡ x)dx=

Correct answer: (D) 0. Let I=∫-(π)/2(π)/2log⁡ (2-sin⁡ x)/(2+sin⁡ x)dx As given function f( x )=log( (2−sinx)/(2+sinx) ) is odd. ⇒I= ∫ f( x )dx=0

Q72 / 150 · MHT CET 2016 · Mathematics

$\int_{- \frac{π}{2}}^{\frac{π}{2}} \log (\frac{2 - \sin x}{2 + \sin x}) d x =$

Let

I = \int_{- \frac{π}{2}}^{\frac{π}{2}} \log (\frac{2 - \sin x}{2 + \sin x}) d x

As given function

f (x) = \log (\frac{2 - \sin x}{2 + \sin x})

is odd.

\Rightarrow I = \int f (x) d x = 0

Hence, the correct answer is option: 'D'.