Curated OER
Roller Coaster Robot
Students calculate the area under a curve. In this calculus instructional activity, students use Riemann sums to find and approximate the area under a curve. They use the derivative and differential equations to solve.
Curated OER
Little Red Corvette
Students investigate the acceleration of a car. In this acceleration of a car lesson, students make a scatter plot of corvette acceleration data. Students find a model to fit the data by taking the integral of the curve...
Curated OER
Lesson #94 Exact Area Under a Curve
Students research Riemann Sums. In this area instructional activity students listen to a lecture on finding the area under a curve. Links to a song about Riemann Sums, and a song titled "Failing My Calculus" are included.
Massachusetts Institute of Technology
Mit: Calculus for Beginners and Artists
Students learn about Calculus concepts through online notes, applets, and dialogs. Topics include derivatives, integrals, linear functions, and derivative applications.
University of Illinois
University of Illinois: The Area Under a Curve
This site explains how to find the area under of a curve.
University of Georgia
University of Georgia: One Grain of Rice Mathematical Project
This is the mathematical tale about Raja, one grain of rice, and how quickly it grows. It includes a mathematical project using a spreadsheet to examine exponential growth and a calculus-based extension that explores area under a curve.
University of Utah
University of Utah: Java Area Applet
Nice site explaining how to find the area under a curve by using a Java applet. The applet computes the area of a figure made of rectangles which approximates the region under the given curve.
Texas Instruments
Texas Instruments: Area Under Curve
This activity will illustrate the idea of using the definite integral to represent the area bounded by a function and the x-axis.
CK-12 Foundation
Ck 12: Analysis: Area Under the Curve
[Free Registration/Login may be required to access all resource tools.] The definition of integration, using limits to calculate the area under a curve.
Interactive Mathematics
Interactive Mathematics: Integration
This lesson puts integration to work. Lessons include integral, derivatives, antiderivatives, and indefinite integrals. The Trapezoidal and Simpson's Rules are highlighted. The examples are enhanced using Live, Math and Scientific...
Wolfram Research
Wolfram Math World: Area
Definitions and formulas for the computation of surface areas of triangles, rectangles, and any regular polygon. Helpful links to related pages.
Analyze Math
Analyze Math: Find Area Under Curve
Scholars examine how to find the area under and between curves using definite integrals. The tutorial consists of practice exercises and examples with solutions.
University of Notre Dame
University of Notre Dame: Approximating Area Under a Curve With Rectangles
PDF of examples for finding the area under a curve using rectangles.
Integrated Publishing
Integrated Publishing: Area Under a Curve
A step-by-step explanation of the formulas needed to find the area under a curve by working through an example problem.
Khan Academy
Khan Academy: Application of Definite Integrals
If you have a function representing rate, what does the area under its curve represent? Area under rate function gives the net change. The definite integral of a rate function gives us the net change in the quantity described by the rate.
Washington State University
Washington State University: Estimate the Area Under a Curve
You can have a good time with this java applet that lets you place adjustable shapes under a curve and then sums the areas to approximate the area of the curve.
University of Colorado
University of Colorado: Normal Probabilities Applet #2
This Applet allows the user to grab and drag the ends of the included region below the standard normal curve to the appropriate places needed. The user directly experiences the connection between the shaded area under the curve and the...
Math Graphs
Houghton Mifflin: Math Graphs: Area of a Region [Pdf]
Students calculate the area of a region using the Midpoint Rule. The resource consists of an enlarged printable version of a graph available in PDF format.
Interactive Mathematics
Interactive Mathematics: Area Under a Curve
Using integration, this tutorial demonstrates how it is possible to find the area under a curve. Several examples are provided to allow for extra practice.
Interactive Mathematics
Interactive Mathematics: Areas by Integration
This tutorial is a more in-depth look at using integrals to determine the area under a curve. Several cases are discussed, including areas of curves that occur below the x-axis and integration using vertical sums.