Antiderivatives / Indefinite Integrals

A tutorial on antiderivatives and indefinite integrals. Covers the Uniqueness Theorem, inverse property and applications of indefinite integrals.

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

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.

Fundamental Theorem of Calculus

Tutorial on the Fundamental Theorem of Calculus.

Techniques of Integration - Substitution

Tutorial on integration using the method of substitution.

Techniques of Integration - Integration by Parts

Tutorial on 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.

Techniques of Integration

Numerical Integration

Tutorial on numerical integration.

Tutorial on numerical integration and error bounds.

Improper Integrals

Tutorial on improper integrals over unbounded intervals.

Tutorial on improper integrals of functions with discontinuities.