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