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In the equation $\int \frac{d x}{\sqrt{2 a x - x^{2}}} = a^{n} \sin^{- 1} (\frac{x}{a} - 1)$ . Find the value of $n$ .

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n=0

n=1

n=2

n=5

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detailed solution

Correct option is A

dx2ax-x2 is dimensionlessTherefore, ansin-1xa-1 should also be dimensionless.Hence, n=0

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In the equation ∫dx2ax-x2=ansin-1xa-1. Find the value of n.

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In the equation $\int \frac{d x}{\sqrt{2 a x - x^{2}}} = a^{n} \sin^{- 1} (\frac{x}{a} - 1)$ . Find the value of $n$ .