Question

Let \( I = \int_{0}^{\frac{\pi}{2}} \log (\cos x) \, dx \)

• A. \( \frac{1}{2} \log (\tan x) \)
• B. \( \frac{1}{2} \log (\sin x) \)
• C. \( \log (\cos x) \)
• D. \( \log (\cos x) + \text{C} \)

Hint:

When solving logarithmic integrals, use the properties of logarithms and trigonometric functions for simplification.

Answer 1

The Correct Option is D

We compute the integral using standard logarithmic and trigonometric identities.