Definite Integral
General
Grade 12
Question:
$\int_{-\pi/2}^{\pi/2} \sin^4 x \cos^6 x \, dx =$
$\frac{3\pi}{64}$
$\frac{3\pi}{572}$
$\frac{3\pi}{256}$
$\frac{3\pi}{128}$
Step-by-Step Solution
Key Concept: General
$I = \int_{-\pi/2}^{\pi/2} \sin^4 x \cos^6 x \, dx = 2 \int_{0}^{\pi/2} \sin^4 x \cos^6 x \, dx = 2 \frac{(3 \cdot 1)(5 \cdot 3 \cdot 1)}{10 \cdot 8 \cdot 6 \cdot 4 \cdot 2} \cdot \frac{\pi}{2} = \frac{3\pi}{256}$
Correct Answer: C