# Activities

• • • ##### Subject Area

• Math: Calculus: Applications of Integral, Antiderivatives and Definite Integrals

• ##### Author 9-12

45 Minutes

Derive™ 6

• ##### Report an Issue

Planting & Harvesting - An Application of the Definite Integral

#### 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.

• 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