Q. 2TF - Calculus

Question

Approximating the length of a curve: Suppose you want to

calculate the driving distance between New York City and

Dallas, Texas.
How could we use the method of “subdivide, approximate, and add up” to approximate this driving distance?

Step-by-Step Solution

Answer

The driving distance can be found using the method of subdivide, approximate, and add up.

Step 1. Given Information

The major route between New York City and Dallas, Texas  by driving distance.

Step 2. Analyzing the subdivided map

The major route between New York City and Dallas, Texas is highlighted in the map above.
The route has been subdivided as:
Dallas-Lake Charles, Lake Charles-New Orleans, New Orleans-Panama City, Panama City-Florida Gulf Coast, Florida Gulf Coast-Miami, Miami-Orlando, Orlando-Savannah, Savannah-Charlotte, Charlotte-Washington DC, Washington DC-New York.

Step 3. Approximate distance of the subdivided routes

The approximate distances 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 4. Adding up the distance

Adding up all the approximate distance found, the total approximate distance between New York City and Dallas, Texas is $2420.7$miles.