Chapter 8: Techniques of Integration - Section 8.8 - Improper Integrals - Exercises 8.8 - Page 501: 27

$$\frac{\pi}{2}$$

\begin{align*} \int_{0}^{2} \frac{d s}{\sqrt{4-s^{2}}}&=\lim _{b \rightarrow 2^{-}} \int_{0}^{b} \frac{d s}{\sqrt{4-s^{2}}}\\ &=\lim _{b \rightarrow 2^{-}}\left[\sin ^{-1} \frac{s}{2}\right]_{0}^{b}\\ &=\lim _{b \rightarrow 2^{-}}\left[\sin ^{-1} \frac{b}{2}-\sin ^{-1} 0\right]\\ &=\frac{\pi}{2}-0=\frac{\pi}{2} \end{align*}