TS EAMCET · Maths · Indefinite Integration
\(\int\left(\sqrt{\frac{a+x}{a-x}}+\sqrt{\frac{a-x}{a+x}}\right) d x\) is equal to
- A \(2 \sin ^{-1}\left(\frac{x}{a}\right)+C\)
- B \(2 a \sin ^{-1}\left(\frac{x}{a}\right)+C\)
- C \(2 \cos ^{-1}\left(\frac{x}{a}\right)+C\)
- D \(2 a \cos ^{-1}\left(\frac{x}{a}\right)+C\)
Answer & Solution
Correct Answer
(B) \(2 a \sin ^{-1}\left(\frac{x}{a}\right)+C\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Let } I=\int\left(\sqrt{\frac{a+x}{a-x}}+\sqrt{\frac{a-x}{a+x}}\right) d x \\ & \text { Put } x=a \cos 2 \theta \Rightarrow d x=-2 a \sin 2 \theta d \theta \\ & \therefore I=-\int\left(\sqrt{\frac{a+a \cos 2 \theta}{a-a \cos 2 \theta}}+\sqrt{\frac{a-a…
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