Physics

$$\int \dfrac { x d x } { \sqrt { 2 a x - x ^ { 2 } } } = a ^ { n } \sin ^ { - 1 } \left[ \dfrac { x } { a } - 1 \right]$$. The value of n is:you may use dimensional analysis to solve the problem


ANSWER

1


SOLUTION
We know,

$$\sin^{-1} $$ is dimensionless quantity.

And,

$$\bigg[\dfrac{x}{a}\bigg]=$$ dimensionless.

[x]=[a],

In LHS,

Dimension is $$=[a]$$ 

And in RHS, 

Dimension is $$=[a]^n$$

Hence it is clear that $$n=1$$

Option $$\textbf C$$ is the correct answer
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