AP EAMCET · Maths · Indefinite Integration
\(\int \sin ^{-1}\left(\sqrt{\frac{x-a}{x}}\right) d x=\)
- A \(x \cos ^{-1} \sqrt{\frac{a}{x}}-\sqrt{a x-a^2}+c\)
- B \(x \sec ^{-1} \sqrt{\frac{a}{x}}+\sqrt{x^2-a x}+c\)
- C \(x \sin ^{-1} \sqrt{\frac{x}{a}}+\sqrt{x^2+a x}+c\)
- D \(\frac{x}{a} \sin ^{-1} \frac{x}{a}+\frac{x^2}{a} \sqrt{1+a^2}+c\)
Answer & Solution
Correct Answer
(A) \(x \cos ^{-1} \sqrt{\frac{a}{x}}-\sqrt{a x-a^2}+c\)
Step-by-step Solution
Detailed explanation
\(I=\int \sin ^{-1}\left(\sqrt{\frac{x-a}{x}}\right) d x\)…
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