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Question: Answered & Verified by Expert
$\int_0^{\pi / 2} \log \left(\frac{4+3 \sin x}{4+3 \cos x}\right) d x=$
MathematicsDefinite IntegrationMHT CETMHT CET 2021 (23 Sep Shift 1)
Options:
  • A 0
  • B $4 \log 3$
  • C $\frac{1}{2}$
  • D $2 \log 4$
Solution:
2603 Upvotes Verified Answer
The correct answer is: 0


Eq. (1) $+(2)$ gives,
$$
2 I=\log \left[\frac{4+3 \sin x}{4+3 \cos x} \times \frac{4+3 \cos x}{4+3 \sin x}\right] d x=\int_0^{\frac{\pi}{2}}(\log 1) d x=0
$$

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