Definite Integration
General
Grade 12
Question:
Evaluate $\int_{0}^{2\pi} \frac{\sin 2x}{\cos 4x + \sin \frac{x}{2}} \, dx$
Step-by-Step Solution
Key Concept: General
$I = \int_{0}^{2\pi} \frac{\sin 2x}{\cos 4x + \sin \frac{x}{2}} \, dx = \int_{0}^{\pi} \left( \frac{\sin 2x}{\cos 4x + \sin \frac{x}{2}} + \frac{-\sin 2x}{\cos 4x + \sin \frac{x}{2}} \right) \, dx = 0$
Correct Answer: 0