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.

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.

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.