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

Toolbox:
• $I=\int \sqrt {a^2-x^2} dx=\frac {x}{2}\sqrt{a^2-x^2}+\frac{a^2}{2} \sin {-1}(\frac{x}{a})+c$
Given $I=\int \sqrt{4-x^2}$

Clearly this is of the for $\sqrt{a^2-x^2}=\frac{x}{2}\sqrt{a^2=x^2}+\frac{a^2}{2}\sin^{-1}(x/9)$

Here $a^2=4\qquad=>a=2$

I=$\frac{x}{2}\sqrt{4-x^2}+\frac{4}{2}\sin^{-1}(\frac{x}{2})+c$

$\qquad=\frac{x}{2}\sqrt{4-x^2}+2 \sin^{-1}(\frac{x}{2})+c$