If x and a represent distance,then for what v | vedclass

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(B) The standard integral formula is $\int \frac{dx}{\sqrt{a^2 - x^2}} = \sin^{-1} \frac{x}{a}$.According to the principle of homogeneity of dimension

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$2$

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(B) The standard integral formula is $\int \frac{dx}{\sqrt{a^2 - x^2}} = \sin^{-1} \frac{x}{a}$.According to the principle of homogeneity of dimensions,terms that are added or subtracted must have the same dimensions.In the denominator,the terms $a^2$ and $x^n$ are subtracted,so they must have the same dimensions.Since both $x$ and $a$ represent distance,their dimension is $[L]$.Therefore,$[a^2] = [L^2]$ and $[x^n] = [L^n]$.Equating the dimensions: $[L^2] = [L^n]$.This implies $n = 2$.

If $x$ and $a$ represent distance,then for what value of $n$ is the given equation dimensionally correct? The equation is $\int \frac{dx}{\sqrt{a^2 - x^n}} = \sin^{-1} \frac{x}{a}$.

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