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Definite Integration

Wallis' Formula

Premium Question

Grade 12

Question:

$\int_0^{\pi/2} \sin^3 x \, dx$ equals:

(1) $\frac{2}{3}$

(2) $\frac{3}{4}$

(3) $\frac{\pi}{4}$

(4) $\frac{1}{3}$

Step-by-Step Solution

Key Concept: Use the reduction (Wallis') formula for $\int_0^{\pi/2} \sin^n x \, dx$ when $n$ is odd, with $n = 3$.

The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.

Correct Answer: (1)