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

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Solution

The correct option is B $2$
From the given equation, using the principle of homogeneity, we can say:
$[a^{2}] = [x^{n}]$
$[L^{2}] = [L^{n}]$
$\Rightarrow n = 2$

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Similar questions

\int \frac{d x}{\sqrt{a^{2} - x^{n}}} = s i n^{- 1} \frac{x}{a}

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\int \frac{d x}{\sqrt{a^{2} - x^{n}}} = {sin}^{- 1} \frac{x}{a}

Let x and a stand for distance. Is $\int \frac{d x}{\sqrt{a^{2} - x^{2}}} = \frac{1}{a} s i n^{- 1} \frac{a}{x}$ dimensionally correct ?

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