Indefinite Integration
Trigonometric Integrals
Premium Question
Grade 12
Question:
If $\int \sin^2 x \cos^3 x \, dx = \frac{\sin^3 x}{3} - \frac{\sin^a x}{a} + C$, the value of $a$ equals _____.
Step-by-Step Solution
Key Concept: Write $\cos^3 x = (1 - \sin^2 x) \cos x$ and substitute $u = \sin x$ to convert the integral into a polynomial integral in $u$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 5