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\[\int \frac{d x}{\sqrt{2 a x-x^{2}}}=a^{n} \sin ^{-1}\left[\frac{x}{a}-1\right]\]The value of \( n \) is(a) 0(b) \( -1 \)(c) 1(d) none of these.You may use dimensional analysis to solve the problem. |
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Answer» \(\int\frac{dx}{\sqrt{2ax-x^2}}\) \(= \int \frac{dx}{\sqrt{a^2 - (x -a)^2}}\) \(= sin^{-1}\left(\frac{x-a}a\right)\) \(= sin^{-1}\left(\frac{x}a -1\right)\) \(\therefore n = 0\) |
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