Curated OER
The Region Between Two Curves
Learners find the area of a region between two curves. They integrate functions such as sin(x) and cos(x) on a given interval and find the area bounded by the two functions. Pupils use their TI-89 to aid them in finding the bounded...
Curated OER
Area Between Two Curves
Twelfth graders identify and find the area between two curves. In this calculus lesson, 12th graders decide what the best way is to find the shaded area between two curves using examples from previous lessons. They relate areas between...
Houston Area Calculus Teachers
Area and Volume
An AP calculus lesson begins with an activity to determine the volume of a solid using a cross-section. Next, learners review the ways to find the area between two curves , as well how to find the volume of a solid created from the...
Alabama Learning Exchange
I'm Lovin' It: Finding Area Between Curves
Students explore the concept of finding the area between two curves. In this finding the area between two curves instructional activity, students model the logos of McDonalds, Nike, and Motorola on grid paper. Students find functions to...
Curated OER
Math 155 - Spring 2002 Worksheet 13: Area of Bounded Regions
In this area worksheet, students solve 3 short answer problems. Students determine the area of a region bounded by two curves.
Curated OER
Area Between Two Curves
Learners investigate the concept area that is found between two curves. They find the area in the top and bottom curve and then examine the differences. The examples can be used for direct instruction and to provide a guide for helping...
Curated OER
Area Between Two Curves
Students engage in a lesson that is concerned with the concept of computing the area between 2 curves with respect to the x and y axis. They concentrate on using positive and negative intervals and find the curve while determining the...
Illuminations
Circumference and Areas of Circles
Middle and high schoolers listen to a scenario about a puppy and use the scenario to develop formulas in order to find the area of a circle. In this circumference lesson, pupils understand how to find the radius, diameter, area of a...
Curated OER
AP Calculus Practice Exam BC Version: Part B
In this calculus worksheet, students solve 17 multiple choice problems. Students find limits, summations, and derivatives of functions. Students find the area of an enclosed region between two curves.
Curated OER
Area of Curve
In this calculus worksheet, students calculate the area of a curve bounded between two regions. There are 2 questions asking for the area and length of a curve.
Curated OER
A.P. Calculus Integration Test
In this A.P. Calculus worksheet, learners complete a sixteen question test covering trigonometric integration, area under a curve, differential equations, and slope fields. Some of the problems are multiple choice, while others are...
College Board
2010 AP® Calculus BC Free-Response Questions Form B
Keep moving along a curve. Two items in the set of released free-response questions from the 2010 AP® Calculus BC exam involve movement along a graph. One involves particle motion along a polar curve while the other uses a squirrel...
Curated OER
Test on Chapter 7
Students review integrals and how they apply to solving equations. In this calculus lesson, students assess their knowledge of area between two curves, arc length, finding the volume using disk, washer and shell method. This assignment...
Curated OER
The Hyperbolic Sine and Cosine
In this sine and cosine worksheet, students find derivatives and integrals of 6 functions. Students find derivatives, indefinite integrals and the area between two curves.
Shodor Education Foundation
Overlapping Gaussians
Adjust the overlap to compare probabilities. Using sliders, learners adjust the shape of two Gaussian curves. The interactive calculates the area of the left tail for one curve and the right tail for the other. Pupils set the interactive...
Curated OER
Shapes and Their Insides
Learners follow a series of instructions for drawing and coloring different shapes in order to learn the difference between the perimeter and area of a polygon. Then they are asked to find the perimeter and area of a 3x4 rectangular...
Balanced Assessment
On Averages and Curves
Determine the average on a curve. The class finds graphical representations of averages and expresses them both symbolically and on the graph. The assessment requires class members to justify using average to describe graphs.
Curated OER
Areas Under Curves: An Astronomical Perspective
In this area under the curve activity, students use a graph of the number of exoplanets discovered and the year they were discovered to solve 5 problems. Students find the total area under the curve, they find the total number of planets...
K12 Reader
World Climates
Why is weather different around the world? Learn about world climates with a reading comprehension passage. Kids read a short passage before answering five comprehension questions based on context clues.
Curated OER
Integrals
In this integrals worksheet, students solve and complete 20 various types of problems. First, they evaluate each of the listed integrals shown. Then, students find the area under the graph given and above the x-axis between two points....
Curated OER
About Faces and Fractions
Third graders review concepts of fractions, and one-half. They discuss self portraits and the relationships of eyes, nose and mouth to the whole face. Students create base-line self-portraits. On the second day, 3rd graders observe and...
Curated OER
Single Event Upsets in Aircraft Avionics
In this aircraft avionics activity, science fans read about the first unmanned air vehicle that collects data about the Earth and is subject to damage by cosmic ray showers. Pupils analyze two graphs of data showing the neutron flux vs....
Illustrative Mathematics
Designs
A resource that makes for excellent group work as students explore the area and perimeter of different complex designs made up of squares and circles. The commentary gives a clear definition of perimeter, but suggests that group members...
Curated OER
Errors in Riemann Sums
In this Riemann Sums worksheet, students use the Riemann Sums method to approximate the area under the curves. This two-page worksheet contains three problems.