Activity Overview
In this activity, students learn and explore how Indefinite integrals are used to find the antiderivative of a function. They also learn that Definite integrals can be used to find the area bounded by a function and the X-axis. From examples they learn that both types of integration can be connected together by the Fundamental Theorem of Integral Calculus.
Before the Activity
See the attached PDF file for detailed instructions for this activity
Print pages 39 - 48 from the attached PDF file for your class
During the Activity
Distribute the pages to the class.
Follow the Activity procedures:
The Area Under a Parabola:
Numerical Method:
Enter the function and graph it
Enter boundaries and number of rectangles
Use left-hand, right- hand, and midpoint Riemann Sums, and approximate the area bounded by the function
Analytical Method:
Define functions for the left-hand, right-hand, and midpoint rectangle methods
Evaluate the functions
Take the limit of each summation function as the number of rectangles approaches infinity
Find both approximate and exact values of the function for the area under the curve for the function
Notice that the area function is the antiderivative of f(x)
Find the area from a to b and predict the definite integral of the function with a and b as boundaries
Area Under other Curves:
Enter the function and find limits of the right-hand Riemann Sum to find the area from a to b
Compare the results with a corresponding definite integral
Notice that the limit of Riemann Sum is related to the antiderivative of the function
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