Peer Review

Calculus - Reimann Sums vs. Trapezoids

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Overview:: This site offers a GeoGebra applet as a tool for helping users to visualize and compare the calculations of the area under a curve using Riemann sums or trapezoids.
Type of Material:: Simulation
Recommended Uses:: The would be a great tool for in-class demonstrations and individual exploration
Technical Requirements:: This applet works well using Microsoft Edge. I had some difficulty getting it to load using Chrome.
Identify Major Learning Goals:: Goals of this tool include helping users to visualize the approximation of the area under a curve using left, right, and midpoint Riemann sums and trapezoids as well as to allow users to compare these approximations.
Target Student Population:: Calculus I students or introductory numerical analysis students.
Prerequisite Knowledge or Skills:: College Algebra, Calculus I

Rating:
Strengths:: This is a very visual and interactive applet. Users can just simply input their own function (can also benefit from the provided mini-keyboard in the applet to help them customize their own function) and can select the interval bounds by entering them in the starting and ending value boxes or by sliding points on the graph. Users can enter the maximum number of subdivisions and then can increase to this number using a slider. The approximated area is displayed as the number of subdivisions increases, allowing users to visualize the approximated area approaching the actual value of the definite integral. Users can check boxes to calculate approximated area using trapezoids, or left, right, or midpoint rectangle sums.
Concerns:: For some users, this applet has a technical issue with chrome browser, although it works well in Edge.

Rating:
Strengths:: This applet is a great visualization tool and could be very useful for in-class demonstrations.
Concerns:: This tool might be improved by providing links to OER resources related to Riemann sums or trapezoid sums.

Rating:
Strengths:: This applet is very interactive and intuitive to use. Users can simply use it without any diffculty.
Concerns:: None