TS EAMCET · Maths · Indefinite Integration
If \(\int \sin ^{-1}\left(\sqrt{\frac{x}{a+x}}\right) d x=A(x)+\) constant, then \(A(x)=\)
- A \(\operatorname{atan}^1 \sqrt{\frac{x}{a}}+a x\)
- B \(\frac{1}{\sqrt{a+x}} \tan ^1 \sqrt{\frac{x}{a}}-\sqrt{a x}\)
- C \((a+x) \tan ^1 \sqrt{x}+a \sqrt{x}\)
- D \((a+x) \tan ^1 \sqrt{\frac{x}{a}}-\sqrt{a x}\)
Answer & Solution
Correct Answer
(D) \((a+x) \tan ^1 \sqrt{\frac{x}{a}}-\sqrt{a x}\)
Step-by-step Solution
Detailed explanation
Let \(I=\int \sin ^2 \sqrt{\frac{x}{a+x}} d x\) Put \(x=a \tan ^2 \theta \Rightarrow d x=2 a \tan \theta \sec ^2 \theta d \theta\)…
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