The Density of Cars (In Cars Per Mile)down a 20-Mile $\rho(x)=500+100 \sin (\pi x)$

Multiple Choice

The density of cars (in cars per mile) down a 20-mile stretch of the Massachusetts Turnpike starting at a toll plaza is given by $\rho(x) =500+100 \sin (\pi x)$ , where x is the distance in miles from the toll plaza and 0 $\le$ x $\le$ 20.Which of the following Riemann sums estimates the total number of cars down the 20-mile stretch?

A) $\sum_{i=0}^{20} \rho\left(x_{i}\right) \Delta x$ , where the 20-mile stretch is divided into n pieces of length $\frac{20}{n}=\Delta x$ , and
$x_{i}$ is a point in the i ^th segment.
B) $\sum_{i=0}^{n-1} n \cdot \rho\left(x_{i}\right)$ , where the 20-mile stretch is divided into n pieces of length $\frac{20}{n}=\Delta x$ , and
$x_{i}$ is a point in the i ^th segment.
C) $\sum_{i=0}^{20} \rho\left(\Delta x_{i}\right)$ , where the 20-mile stretch is divided into n pieces of length $\frac{20}{n}=\Delta x$ , and
$x_{i}$ is a point in the i ^th segment.
D) $\sum_{i=0}^{n-1} \rho\left(x_{i}\right) \Delta x$ , where the 20-mile stretch is divided into n pieces of length $\frac{20}{n}=\Delta x$ , and
$x_{i}$ is a point in the i ^th segment.