Chapter 8 - Techniques of Integration - 8.7 Improper Integrals - Exercises - Page 440: 11

$$4$$

\begin{aligned} \int_{0}^{4} \frac{d x}{\sqrt{4-x}} &=\lim _{R \rightarrow 0} \int_{R}^{4} \frac{d x}{\sqrt{4-x}} \\ &=\lim _{R \rightarrow 0} \int_{R}^{4} \frac{(-2) d x}{(-2) \sqrt{4-x}} \\ &= \lim _{R \rightarrow 0} -2\sqrt{4-x} \bigg|_{0}^{4}\\ &= \lim _{R \rightarrow 0} 2\sqrt{4-R}\\ &=4 \end{aligned}