Answer
$$2 \sqrt{2}$$
Work Step by Step
\begin{aligned}
\int_{1}^{3} \frac{d x}{\sqrt{3-x}} &=\lim _{R \rightarrow 3} \int_{1}^{R} \frac{d x}{\sqrt{3-x}} \\
&=\lim _{R \rightarrow 3}- 2 \sqrt{3-x}\bigg|_{1} ^{R} \\
&=\lim _{R \rightarrow 3} 2 \sqrt{2}-2 \sqrt{3-R} \\
&=2 \sqrt{2}\end{aligned}
Converges.
