Integrate the function: $\sqrt{4-x^{2}}$

(N/A) Let $I = \int \sqrt{4-x^{2}} \, dx = \int \sqrt{(2)^{2}-(x)^{2}} \, dx$.
We use the standard integration formula: $\int \sqrt{a^{2}-x^{2}} \, dx = \frac{x}{2} \sqrt{a^{2}-x^{2}} + \frac{a^{2}}{2} \sin^{-1} \left(\frac{x}{a}\right) + C$.
Here,$a = 2$.
Substituting $a = 2$ into the formula:
$I = \frac{x}{2} \sqrt{4-x^{2}} + \frac{4}{2} \sin^{-1} \left(\frac{x}{2}\right) + C$.
Simplifying the expression:
$I = \frac{x}{2} \sqrt{4-x^{2}} + 2 \sin^{-1} \left(\frac{x}{2}\right) + C$,where $C$ is an arbitrary constant.