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General
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| | Definite Integrals
This is an excellent tutorial on evaluating a definite integral by setting up Riemann sums and finding their limits (that is, evaluation without using the Fundamental Theorem of Calculus). The applets take the viewer step by step through the process with drawings to accompany the equations.
 Definite Integrals
The Definite Integral
This page is part of a site maintained by Sandra Halfacre of White Station High School in Memphis, Tennessee. This particular page contains links to tutorials, slide shows, animations, and applets helping students to understand the concept of a definite integral. There are numerous links to pages explaining Riemann sums, the Trapezoid Rule, the Fundamental Theorem of Calculus, and properties of the definite integral.
The Definite Integral
Numerical Integration
Authors Stefan Waner and Steven Costenoble, both from Hofstra University, provide an instructive tutorial on left and right Riemann sums and the Trapezoidal Rule.
Numerical Integration
The Integrator
The Integrator is powered by Mathematica and is part of the Wolfram Research Resource Library. Users simply enter an integrand and click the appropriate button, and the answer appears in standard form. There is a short history of integration and only a few examples of integrals at work. The site provides instructions for entering expressions and will automatically choose random examples.
The Integrator
TI Graphing Calculator FAQ -- Riemann Sums
This site contains routines and programs for computing Riemann sums on Texas Instruments calculators. It contains a program for the TI-82/83 (Plus) calculators and routines based on defined functions for the TI-89/92 (Plus) and TI-86 calculators. These compute the left, right, and midpoint Riemann sums. They also compute the Trapezoid and Simpson's Rule approximations for the definite integral.
TI Graphing Calculator FAQ -- Riemann Sums
Improper Integration
This site guides the user through an investigation of four improper integrals that all involve arctan(1/t). The tutorial suggests creating a table of values for each problem and prods the user to think about why certain integrals converge and others do not. These problems might make a nice homework assignment while studying improper integrals.
Improper Integration
Substitution in the Indefinite Integral
This tutorial does a very through job of explaining u-substitutions for finding antiderivatives. The process is illustrated by three examples in which the student is asked interactive, multiple-choice questions at each step in the process. This is a good place to start learning the procedure, but naturally more practice will be needed.
Substitution in the Indefinite Integral
Integration by Parts
This site presents a brief derivation of and introduction to integration by parts. There are no hints as to how one should choose the functions u or dv. The presentation suggests that experimentation and experience are the best teachers. The mathematical notation is easy to follow here, and there are several links to examples at the end of the material.
Integration by Parts
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