Question

\[\int\frac{dx}{\sqrt{2ax - x^2}} = a^n \sin^{- 1} \left[ \frac{x}{a} - 1 \right]\] 
The value of n is

Options

• 0

• -1

• 1

• none of these.

Answer 1

0
[ax] = [x²]
⇒ [a] = [x]    ...(1)
Dimension of LHS = Dimension of RHS

\[\Rightarrow \left[ \frac{dx}{\sqrt{x^2}} \right] = \left[ a^n \right]\]

\[ \Rightarrow \left[ \frac{L}{L} \right] = \left[ a^n \right] . . . (2) \]

\[[ L^0 ] = [ a^n ]\]

\[n = 0\]