Question

The value of $\int _ { 0 } ^ { \pi / 2 } \log \left( \frac { 4 + 3 \sin x } { 4 + 3 \cos x } \right) d x$ is

• A. 2
• B. $\frac { 3 } { 4 }$
• C. 0
• D. None of these

Answer 1

Answer: (C)

0

Answer 2

Let

Then, $I = \int _ { 0 } ^ { \pi / 2 } \log \left( \frac { 4 + 3 \cos x } { 4 + 3 \sin x } \right) d x$,

$\left[ \because \int _ { 0 } ^ { \pi / 2 } f ( x ) d x = \int _ { 0 } ^ { \pi / 2 } f \left( \frac { \pi } { 2 } - x \right) d x \right]$

⇒ $I = - \int _ { 0 } ^ { \pi / 2 } \log \left( \frac { 4 + 3 \sin x } { 4 + 3 \cos x } \right) d x = - I$

⇒ $2 I = 0 \Rightarrow I = 0$.