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Let x and a stand for distance. Is

Question:

Let $\mathrm{x}$ and a stand for distance. Is

$\int \frac{d x}{\sqrt{a^{2}-x^{2}}}=\frac{1}{a} \sin ^{-1} \frac{a}{x}$ dimensionally correct?

Solution:

Dimension of the Integral $=\int \frac{d x}{\sqrt{a^{2}-x^{2}}}=\int \frac{L}{\sqrt{L^{2}-L^{2}}}=L^{0}$. But for $\frac{1}{a} \sin ^{-1} \frac{a}{x}$, the dimension is [L-1]. So

this expression is dimensionally incorrect.

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