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  4. If x and a stand for distance, then for what value of n is the given equation dimensionally correct? The equation is ∫ (d x/√a2-xn)= sin -1 (x/a)

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

Physical World, Units and Measurements

Solution:

Here $x^{n}$ has the same dimensions as $a^{2}$.
Thus, $n=2$ will make the expression dimensionally correct.