**Antiderivatives / Indefinite Integrals**- A tutorial on antiderivatives and indefinite
integrals. Covers the Uniqueness Theorem, inverse property and applications
of indefinite integrals.
- Table of Elementary Indefinite Integrals
- An example illustrating the evaluation of an indefinite integral using
properties of indefinite integrals.

[using Flash] - Drill on evaluating simple integrals using the Table of Elementary Integrals.

[Using Java] [Using IBM TechExplorer] [Using IBM Pro. TechExplorer] - Drill on evaluating simple integrals with initial conditions.

[Using Java] [Using IBM TechExplorer] [Using IBM Pro. TechExplorer] - Application of indefinite integrals.

[using Flash] - Another application of indefinite integrals.

[using Flash]

A tutorial on slope fields with an interactive JAVA applet to explore slope fields.

- An interactive LiveMath notebook that graphs the slope field for a function and graphs antiderivatives.
- A computer program that graphs the slope field for a function.
- Another computer program that graphs the slope field for a function and graphs antiderivatives.
- An animation illustrating the different solutions for indefinite integrals using slope fields.
- Using a TI-86 graphing calculator to graph slope fields and the antiderivative
of a function.

[using Flash] - TI-85 graphing calculator programs to graph slope fields.

**Areas**- A tutorial on how to find areas and approximation
to areas by using inscribed and circumscribed rectangles.
- An animation illustrating the approximation of the area under the sine function by inscribed and circumscribed rectangles.
- An animation illustrating the approximation of the area under a parabola by inscribed and circumscribed rectangles.
- A computer program that illustrates the approximation of the area of a circle using inscribed polygons.
- An animation showing the approximation of the area of a circle using inscribed polygons.
- A computer program that graphically illustrates the Monte Carlo Method to find areas.

**Riemann Sums**- A tutorial on riemann sums from
the graphical point of view followed by a
tutorial from a symbolic or algebraic point of view.
- A tutorial on summations and summation notation.
- Drill in finding Riemann Sums of linear functions (using IBM TechExplorer)
- An example of a sum evaluated using the TI-85 or TI-86 graphing calculator.
- Another example of a sum evaluated using the TI-85 or TI-86 graphing calculator.
- An interactive LiveMath Notebook to evaluate Riemann Sums.
- Using a graphing calculator to evaluate Riemann Sums.
- Computer software that graphically illustrates the use of Riemann sums to approximate the area bounded by the graph of a function and the x-axis and a couple of lines.
- Computer software that graphically and numerically approximate an area.
- Computer software that graphically and numerically approximate an area by evaluating upper and lower Riemann sums.

**Definite Integrals**- A tutorial on the definition of definite
integrals, properties of definite integrals, relationship between definite
integrals and areas and the use of technology to evaluate definite integrals
using the definition.
- A Flash movie illustrating the evaluation of a definite integral using
the definition.

[using Flash] [using Java] - A Flash movie illustrating the finding the area by using the definition of a definite integral.
- Using a computer algebra system and Riemann sums to evaluate definite integrals.
- Computer software that can symbolically evaluate an integral using Riemann Sums.

- A Flash movie illustrating the evaluation of a definite integral using
the definition.
**Fundamental Theorem of Calculus**- Tutorial on the Fundamental Theorem of Calculus.
- Examples illustrating use of the Fundamental Theorem of Calculus to evaluate definite integrals.
- Drill problems on evaluating definite integrals using the Fundamental
Theorem of Calculus.

[Using Java] [Using IBM TechExplorer] [Using IBM Pro. TechExplorer] - A interactive Java applet to graphically illustrate the Fundamental Theorem of Calculus.
- An animation illustrating the Fundamental Theorem of Calculus.

[Using animated gifs] [Using LiveMath] - Using the graphing calculator to illustrate graphically the Fundamental Theorem of Calculus.
- An interactive LiveMath Notebook illustrating graphically the Fundamental Theorem of Calculus.
- A Maple animation illustrating graphically the Fundamental Theorem of Calculus.
- Computer programs that graphically illustrate the Fundamental Theorem of Calculus.
- Computer algebra systems and to what extent does Maple "knows" the Fundamental Theorem of Calculus.
- An interactive LiveMath Notebook which can be used to investigate to what extent the program MathView "knows" the Fundamental Theorem of Calculus.
- An interactive LiveMath Notebook which evaluates the derivative of a function which is an integral with variable limits.

**Techniques of Integration - Substitution**- Tutorial on integration using the
method of substitution.
- Drill problems for integration using the method of substitution.
- Quiz on substitutions and elementary integrals.
- Drill on evaluating certain integrals.

[Using Java] [Using IBM Techexplorer] [Using IBM Pro. Techexplorer] - Drill problems for integration using the method of trigonometric substitution.
- Using Maple to illustrate the method of substitution.

**Techniques of Integration - Integration by Parts**- Tutorial on using Integration by
Parts.
- Some drill problems using Integration by Parts.

[Using Java] [Using IBM TechExplorer] [Using IBM Pro. TechExplorer] - Some drill problems using Integration by Parts.

[Using Java] [Using IBM TechExplorer] [Using IBM Pro. TechExplorer] - Some drill problems using Integration by Parts.

[Using Java] [Using IBM Pro. TechExplorer] - Some more drill problems using Integration by Parts.
- Derivation of Integration by Parts formula (uses dynamic html).
- Using Maple to illustrate the method of Integration by Parts.

- Some drill problems using Integration by Parts.
**Techniques of Integration - Reduction Formulas**- Tutorial on deriving and using recursion
or reduction formulas.
- Drill problems for evaluating trigonometric integrals using recursion or reduction formulas.
- Using Maple to obtain some reduction formulas.

**Techniques of Integration - Partial Fractions**- Tutorial on the method of Partial
Fractions.
- Examples illustrating the the method of Partial Fractions.
- Some drill problems

[Using Java] [Using IBM TechExplorer] [Using IBM Pro. TechExplorer] - Drill problems for integration using the method of Partial Fractions.

**Techniques of Integration**-
- Using Maple to evaluate indefinite integrals.

**Numerical Integration**- Tutorial on numerical integration.
- An animation illustrating graphically the Trapezoidal Rule.
- Using a graphing calculator to illustrate the use of the Trapezoidal Rule.
- Computer programs that graphically illustrate the use of the Trapezoidal Rule.
- An animation illustrating graphically Simpson's Rule.
- Using a graphing calculator to illustrate the use of the Simpson's Rule.
- Computer programs that graphically illustrate the use of Simpson's Rule.
- Computer programs that numerically illustrate the use of Simpson's Rule.
- TI-85 graphing calculator programs for numerical integration.
- An interactive LiveMath Notebook to approximate integrals using the Midpoint Rule.
- Computer programs that provide a graphical illustration of the Midpoint Rule.

- Tutorial on numerical integration and
error bounds.
**Improper Integrals**- Tutorial on improper integrals over
unbounded intervals.
- Drill problems on evaluating improper integrals over unbounded intervals. [Using Java][Using IBM Pro. Techexplorer]
- Drill problems on evaluating improper integrals over unbounded intervals.

- Tutorial on improper integrals of functions with discontinuities.