Question
$\int \frac{d x}{\sqrt{a^{2}-x^{2}}}=\frac{1}{a} \sin ^{-1} \frac{a}{x}$(A) is dimensionally correct.(B) dimensionally incorrect.(C) such mathematical relations cannot be tested.(D) cannot say.
Step 1
The left side of the equation is $\int \frac{d x}{\sqrt{a^{2}-x^{2}}}$. Here, $x$ and $a$ represent distance. So, the dimension of the left side would be $L$ divided by the square root of $L^2$, which simplifies to $L^0$ or dimensionless. Show more…
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