Question

Solve: $\int \sqrt{4-x^2}dx$

Answer 1

$\int \sqrt{4-x^2}dx=\int \sqrt{2^2-x^2}dx=[\frac{x\sqrt{4-x^2}}{2}+\frac{2^2}{2}{\text{sin}}^{-1}(\frac{x}{2})]+C=\frac{x}{2}\sqrt{4-x^2}+2{\text{sin}}^{-1}(\frac{x}{2})+C$