Q. 3 - Calculus

Question

Approximating the length of a curve: Suppose you want to calculate the driving distance between New York City and Dallas, Texas.
Make an actual approximation of the driving distance from New York City to Dallas, Texas, using the route and method you just described.

Step-by-Step Solution

Answer

The total distance between New York City and Dallas, Texas is $2420.7$miles.

Step 1. Given Information

Major route between New York City and Dallas, Texas by driving.

Step 2. The subdivided routes

The route between New York City and Dallas, Texas has been highlighted above.
The $10$ subdivided routes are:
Dallas-Lake Charles $345.3$miles
Lake Charles-New Orleans $205.4$miles
New Orleans-Panama City $329.2$miles
Panama City-Florida Gulf Coast $5.8$miles
Florida Gulf Coast-Miami $141.7$miles
Miami-Orlando $235.9$miles
Orlando-Savannah $280.5$miles
Savannah-Charlotte $251.9$miles
Charlotte-Washington DC $400.1$miles
Washington DC-New York $224.9$miles

Step 3. Finding the total distance

By using the method of "subdivide, approximate and add up"
The total distance is $=\sum _{i=1}^{n-10}{x}_i$$\sum _{i=1}^{n-10}=345.3+205.4+329.2+5.8+141.7+235.9+280.5+251.9+400.1+224.9$

 $\sum _{i=1}^{n=10}{x}_i=2420.7$miles.