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

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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Single Correct Medium Published on 18th 08, 2020
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