Chapter 7 - Integration - 7.3 Area and the Definite Integral - 7.3 Exercises - Page 384: 19

$24$

\[\begin{align} & \int_{2}^{5}{\left( 1+2x \right)dx} \\ & \text{The integral represents the area shown below}\text{.} \\ & \text{We can define the area as follows:} \\ & A=\text{area of the rectangle}+\text{area of the triangle} \\ & A=bh+\frac{1}{2}BH \\ & A=\left( 5-2 \right)\left( 5-0 \right)+\frac{1}{2}\left( 5-2 \right)\left( 11-5 \right) \\ & A=24 \\ \end{align}\]