Planting & Harvesting - An Application of the Definite Integral

Published on
06/09/2008

Activity Overview

In this Derive™ activity, students apply the concept of definite integration and decide when a farmer should plant and harvest a crop of clover.

Before the Activity

See the attached DFW file for detailed instructions for this activity

Print pages from the attached DFW file for your class

During the Activity

Distribute the pages to the class.

Follow the Activity Procedures:

Set up a 2D plot window

Determine the latitude and longitude for the location and calculate the hours of sunlight during each day of the year for that location

Plot the data and observe that the graph is a sinusoidal curve

Determine the latitude and longitude of your position and write an expression for the number of daylight hours on spring equinox, autumn equinox, winter solstice, and summer solstice

Write an expression for the hours of daylight on day, t

Sum the values of the function over an interval of days

Take a representative value for the hours of daylight for each day, and add the values

Represent this sum graphically and plot the data about the tops of rectangles

Realize that the sum of the areas of the rectangles is the same as the area under the curve

Understand that the area under the curve is the total number of hours of daylight

Recognize the fact that the value of the definite integral and the value of the sum is the same

Complete the farmer's schedule and determine the dates for the first and second cuttings of clover

After the Activity

Students answer questions listed on the activity sheet.

Review student results:

As a class, discuss questions that appeared to be more challenging