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$\int \frac{dt}{\sqrt{2 at - t^{2}}} = a^{x} \sin^{- 1} [\frac{t}{a} - 1]$ The value of x is

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Correct option is C

The quantity ta - 1 is dimensionless i.e; [a] = [t] ∴ [2at-t2] = [t]or [dt2at-t2] = [tt] = [M0L0T0]i.e ax should also be dimensionless or x = 0

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∫dt2at-t2 = axsin-1[ta-1] The value of x is

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$\int \frac{dt}{\sqrt{2 at - t^{2}}} = a^{x} \sin^{- 1} [\frac{t}{a} - 1]$ The value of x is