Given that ∫dx/√(2ax-x^2 ) = a^n sin^(-1) [(x-a)/a] where a is constant. Using dimensional analysis, value of n is

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Q: Given that $\int \frac{dx}{\sqrt{2ax-x^2}} = a^n sin^{-1}(\frac{x-a}{a})$ , where a is constant. Using dimensional analysis, value of n is

(a) 1

(b) –1

(c) 0

(d) 2

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Ans: (c)
Sol: It is clear from question that constant a has dimension of x , therefore left hand side has no dimension . According to rule right hand side should not have dimension . Hence value of n = 0

 

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