Answer
\[A=2\]
Work Step by Step
\[\begin{align}
& \text{From the graph the region R is given by} \\
& x\le y\le 2x \\
& 0\le x\le 2 \\
& \text{Using an iterated integral we can define the area as:} \\
& A=\int_{0}^{2}{\int_{x}^{2x}{dy}dx} \\
& \text{Integrating} \\
& A=\int_{0}^{2}{\left( 2x-x \right)dx} \\
& A=\int_{0}^{2}{xdx} \\
& A=\left[ \frac{1}{2}{{x}^{2}} \right]_{0}^{2} \\
& A=\frac{1}{2}\left[ {{\left( 2 \right)}^{2}}-{{\left( 0 \right)}^{2}} \right] \\
& A=2 \\
\end{align}\]
