AP EAMCET · Maths · Indefinite Integration
If \(\int \frac{x^{\frac{1}{2}}}{\sqrt{a^3-x^3}} d x=P(x)+c\), then \(\mathrm{P}(x)=\)
- A \(\frac{1}{3} \operatorname{Sin}^{-1}\left(\frac{x^3}{a^3}\right)\)
- B \(\frac{2}{3} \operatorname{Cos}^{-1}\left(\frac{x}{a}\right)\)
- C \(\frac{2}{3} \operatorname{Sin}^{-1}\left(\frac{x}{a}\right)^{\frac{3}{2}}\)
- D \(4^{\frac{1}{3}} \operatorname{Sin}^{-1}\left(\frac{x}{a}\right)^{\frac{1}{2}}\)
Answer & Solution
Correct Answer
(C) \(\frac{2}{3} \operatorname{Sin}^{-1}\left(\frac{x}{a}\right)^{\frac{3}{2}}\)
Step-by-step Solution
Detailed explanation
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