Activity Overview
In this activity students investigate various applications of integration. They learn and explore to use analytic method as well as numerical, and graphical methods for solving various mathematical problems.
Before the Activity
- See the attached PDF file for detailed instructions for this activity
- Print pages 49 - 58 from the attached PDF file for your class
- For Newton's law of cooling activity, connect the Temperature Sensor into channel 1 of the CBL 2™ and start the DataMate program
During the Activity
Distribute the pages to the class.
Follow the Activity procedures:
Area between two Curves:
Graph the two equations and find values for the left and right intersection points
Evaluate the definite integral to find the area between the two curves
Finding Arc Length:
Use the built-in Arc feature to find the arc length
Enter the equation and graph it
Evaluate the expression for the definite integral and compare results
First and second order differential equations:
Toss a ball straight up from an initial height and at an initial velocity
Find an equation to model the height of the ball over time
Scatter Plots and Regression Curves:
Use the Data/Matrix Editor and enter the data values
Solve the equation and graph the data
Find a quadratic regression equation and compare the equations
Newton's Law of Cooling:
Temperature probe is heated and then placed in cold water
Measure the temperature after 30 seconds and find the temperature after 60 seconds
Solve the equation and find the constant of proportionality
Resistance Proportional to velocity:
A ball is dropped from a height of 75 meters
Find when the ball will hit the ground
Logistic Growth:
Given that the rate of growth of a population is directly proportional to both the population and the carrying capacity minus the population
Determine the time period required to reach a certain population size by solving the differential equation
After the Activity
Students will complete the practice exercise problems
Review student results
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary