Integrals
RS Aggarwal
CBSE
Grade 12
Question:
$\int \frac{dx}{\sqrt{9 - 25x^2}}$ is equal to:
(a) $\frac{1}{5} \sin^{-1}\left(\frac{5x}{3}\right) + C$
(b) $\sin^{-1}\left(\frac{5x}{3}\right) + C$
(c) $\frac{1}{3} \sin^{-1}\left(\frac{5x}{3}\right) + C$
(d) $\frac{1}{5} \cos^{-1}\left(\frac{5x}{3}\right) + C$
Step-by-Step Solution
Key Concept: Factor out 25: (1/5) \sin^{-1}(5x/3) + C.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: $\frac{1}{5} \sin^{-1}\left(\frac{5x}{3}\right) + C$
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