Topic: Electronics Engineering
What does the following integral evaluate to?
$\int_{0}^{\pi/2}sin^{6}\theta\cdot d\theta$
- A. $5\pi/16$
- B. $5~\pi/8$
- C. 0
- D. $5~\pi/32$
Answer: D. $5~\pi/32$
Explanation: Using Wallis' integral formula for even powers of sine: $\int_{0}^{\pi/2}sin^{6}x~dx = \frac{5}{6}\cdot\frac{3}{4}\cdot\frac{1}{2}\cdot\frac{\pi}{2} = \frac{5\pi}{32}$.