Question

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

• A. 0
• B. -1
• C. 1
• D. none of these

Answer 1

The correct option is C 1

We know,

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

And,

$[\frac{x}{a}]=$ dimensionless.

[x]=[a],

In LHS,

Dimension is $=\left[a\right]$

And in RHS,

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

Hence it is clear that $n=1$

Option $\text{C}$ is the correct answer