Integrals
Approximating Integrals with Riemann Sums
This activity from Texas Instruments is a good way to help them explore Riemann sums while learning to better use their calculators. You will have to load a program onto each calculator before doing the activity.
Click on the image above to go to the site to download the necessary files.
Click on the image above to go to the site to download the necessary files.
Geometer's Sketchpad: Rectangular and Trapezoidal Area Approximations
I developed a lesson for this Geometer's Sketchpad activity, because it builds a natural motivation for Riemann Sums. Students usually find them very complicated at first glance and thus are reluctant to learn to use them. Counting squares can get tedious, which leads to using rectangles and trapezoids. Eventually that gets tedious, which leads to looking for even faster (and more accurate) ways to approximate the area.
Click on the image above to find the sketch and activity files.
Click on the image above to find the sketch and activity files.
approximating_area_under_a_curve_lesson_plan.docx | |
File Size: | 18 kb |
File Type: | docx |
Area Under a Curve Demo
Students can use this demo to explore the relationship between the area accumulated under a curve, and the area function. By changing the limits of integration, they can see what how the area function changes. Comparing the two graphs side-by-side allows for a discussion of integrals and their derivatives, leading into the Fundamental Theorem of Calculus.
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Area Function for a Piecewise Curve from the Wolfram Demonstrations Project by Charles E. Oelsner |
area_under_a_curve_online_activity_review.docx | |
File Size: | 17 kb |
File Type: | docx |
The Integral Mean Value Theorem: An Illustration from the Wolfram Demonstrations Project by Paul Rosemond |
Integral Mean Value Theorem Demo
This demo provides a visualization of the Integral Mean Value Theorem. Students can see the relationship of the area under the curve, the area of the rectangle and the point where the rectangle crosses the curve.
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mean_value_theorem_integrals_online_activity_review.docx | |
File Size: | 17 kb |
File Type: | docx |
Calculus Game
Jeopardy is always a fun way to review in class, and this demo from the Wolfram Demonstrations Project lets you do just that. The categories are all about integration (integrals, FTC, area between curves, etc.), and you can choose to play for double the points. The Calculus Game Demo also keeps score for you!
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Calculus Game from the Wolfram Demonstrations Project by Michael Sollami |
calculus_game_online_activity_review.docx | |
File Size: | 17 kb |
File Type: | docx |
Solids of Revolution from the Wolfram Demonstrations Project by Abby Brown |
Solids of Revolution Demo
Students often have a difficult time visualizing solids of revolution, especially girls. This is a great tool for helping students understand what we mean by revolving areas around different axes in order to create a solid. This demo includes two different regions, the ability to make the solid translucent and view it from front and back.
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