Definite Integration
General
Grade 12
Question:
Evaluate $\int_{0}^{\pi/2} \cos^6 x \, dx$.
Step-by-Step Solution
Key Concept: General
Using Walli's Theorem for $n = 6$ (even):<br>$I = \frac{5 \cdot 3 \cdot 1}{6 \cdot 4 \cdot 2} \cdot \frac{\pi}{2} = \frac{15}{48} \cdot \frac{\pi}{2} = \frac{5}{16} \cdot \frac{\pi}{2} = \frac{5\pi}{32}$
Correct Answer: $\frac{5\pi}{32}$