Definite Integration
Properties of Definite Integrals
Premium Question
Grade 12
Question:
$\int_0^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx$ equals:
(1) $\frac{\pi}{4}$
(2) $\frac{\pi}{2}$
(3) $\frac{\pi}{8}$
(4) $0$
Step-by-Step Solution
Key Concept: Apply the King's-rule substitution $x \to \frac{\pi}{2} - x$ to obtain a second expression for the same integral, then add it to the original.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)