Education Technology

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
  • Re-teach concepts as necessary