Worksheet
Curated OER

Surface Water

For Students 7th - 10th
In this surface water worksheet, students review water runoff, drainage basins, and river erosion. This worksheet has 7 multiple choice and 3 fill in the blank questions.
Unit Plan
Khan Academy

Khan Academy: Area Between Curves

For Students 9th - 10th
By integrating the difference of two functions, you can find the area between them. Created by Sal Khan.
Activity
Other

Area Between Curves

For Students 9th - 10th
Site explains using an example how to find the area between curves using a calculator.
Activity
Analyze Math

Analyze Math: Find Area Under Curve

For Students 9th - 10th
Scholars examine how to find the area under and between curves using definite integrals. The tutorial consists of practice exercises and examples with solutions.
Lesson Plan
Texas Instruments

Texas Instruments: Area Between Curves

For Teachers 9th - 10th
This activity will illustrate the idea of using the definite integral to represent the area bounded by two curves.
Lesson Plan
Texas Instruments

Texas Instruments: Area Between the Curves the Game

For Teachers 9th - 10th
This activity is set up as a game in which paired students each pick a function and predict the area between the two curves without knowing the other person's function. The students then find the area between the functions and determine...
Handout
Other

Ostermiller.org: Between Curves Tools

For Students 9th - 10th
This site provides instructions for programs you can put into a graphing calculator to find the area between curves.
Activity
Interactive Mathematics

Interactive Mathematics: Area Between 2 Curves

For Students 9th - 10th
Using integration, the area between two curves can be determined. This tutorial illustrates exactly how that can be done through several detailed examples.
Handout
Savvas Learning

Math Centre: Finding Areas by Integration

For Students 10th - 12th
A PDF resource that includes an introduction to finding the area between two curves with examples
Lesson Plan
Alabama Learning Exchange

Alex: I'm Lovin' It: Finding Areas Between Curves

For Teachers 9th - 10th
Students will best fit equations to a curve to find the area of a logo or image. Images will include McDonalds, Nike, and the Motorola logo. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project...
Handout
Paul Dawkins

Paul's Online Notes: Calculus I: Area and Volume Formulas

For Students 9th - 10th Standards
The tutorial examines the area between two curves and the volume of a solid of revolution. The class notes are available in pdf format.
Activity
Texas Instruments

Texas Instruments: The Region Between Two Curves

For Teachers 9th - 10th
This activity is an application of integration. Students use calculus to find the area of a region and the volumes of solids generated by the region. They use the CAS of their TI-89 and calculus to determine the exact answers.
Unknown Type
Khan Academy

Khan Academy: Normal Distribution: Area Between Two Points

For Students 9th - 10th Standards
Use a z-table to find the probability that a particular measurement is in a range. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Unit Plan
Massachusetts Institute of Technology

Mit: Open Course Ware: Appropriate Integrals

For Students 9th - 10th
The activity investigates appropriate integrals. Some topics examined are areas between curves, the disk method, the washer method, and the shell method. All documents were created from scanned original files and are available as PDF...
Activity
Texas Instruments

Texas Instruments: Area Under the Curve

For Teachers 9th - 10th
In this activity, students explore the relationship between the area under the graph of a function and the integral of the function.
Activity
Texas Instruments

Texas Instruments: Applications of Integrals

For Teachers 9th - 10th
Use the TI-89 to find the area between curves, find arc length, and solve first and second order differential equations. Examples in the activity use calculator screenprints and keystroke instructions to demonstrate the use of the...
Handout
Paul Dawkins

Paul's Online Notes: Calculus I: Applications of Integrals

For Students 9th - 10th Standards
The tutorial investigates applications of integrals. Topics discussed are average function value, area between two curves, volumes of solids of revolution, and work. Class notes, definitions, and examples with detailed solutions are...
Activity
Texas Instruments

Texas Instruments: Using Derive

For Teachers 9th - 10th Standards
In this activity, students use the Derive software to solve trigonometric equations, expressions with exponentials, and log equations. They also determine the equation of tangent and normal of a function; evaluate integrals, find area...
App
University of Colorado

University of Colorado: Normal Probabilities Applet #2

For Students 9th - 10th
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...
Activity
Stefan Warner and Steven R. Costenoble

Finite Mathematics & Applied Calculus: Topic Summaries: Techniques and Applications of the Integral

For Students 9th - 10th
The topic summary outlines techniques and applications of integration. Some topics reviewed are integration by parts, area between two curves, and improper integrals. The resource consists of definitions, notes, and examples.

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