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

\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.

Find the Area Inside the Three-Petal Rose r=3cos⁡3θr=3 \cos 3 \thetar=3cos3θ

Short Answer