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GUJCET · Maths · Integrals
\(\int \frac{1}{\sqrt{4 x-x^2}} d x=\) __________ \(+c\).
- A \(\frac{1}{2} \tan ^{-1}\left(\frac{x-2}{2}\right)\)
- B \(\sin ^{-1}\left(\frac{x-2}{2}\right)\)
- C \(\log \left|x-2+\sqrt{4 x-x^2}\right|\)
- D \(\frac{1}{4} \log \left|\frac{x}{x-4}\right|\)
Answer & Solution
Correct Answer
(B) \(\sin ^{-1}\left(\frac{x-2}{2}\right)\)
Step-by-step Solution
Detailed explanation
\(\int \frac{1}{\sqrt{4 - (x-2)^2}} d x\) \(= \sin^{-1}\left(\frac{x-2}{2}\right) + c\)
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