Texas Instruments
Texas Instruments: Approximating Integrals With Riemann Sums
In this activity, students calculate Riemann sums. They demonstrate when the Riemann sums will over-approximate a definite integral. They also observe the convergence of Riemann sums as the number of subintervals get larger.
Texas Instruments
Texas Instruments: Fundamental Theorem of Calculus
In this activity, students explore the connection between an accumulation function, one defined by a definite integral, and the integrand. They also discover that the derivative of the accumulator is the integrand.
Texas Instruments
Texas Instruments: Exploring the Fundamental Theorem of Calculus
In this Derive activity, students investigate the Fundamental Theorem of Calculus and explore examples of Riemann Sums for approximating the Definite Integral: the Midpoint Sum, the Left Hand Endpoint Sum, the Right Hand Endpoint Sum,...
Wolfram Research
Wolfram Mathworld: Definite Integral
Good site explaining the definite integral. This site also gives the integration rules for Definite Integrals, along with definitions and examples.
University of British Columbia
Ubc: The Definite Integral
This site is a tutorial on the definite integral.
Wolfram Research
Wolfram Math World: Indefinite Integral
This MathWorld site offers an explanation of the indefinite integral. Includes links to related topics within the explanation.
Analyze Math
Analyze Math: Definition of Definite Integrals Riemann Sums
The applet examines the definition of the definite integral.
Khan Academy
Khan Academy: Application of Definite Integrals
If you have a function representing rate, what does the area under its curve represent? Area under rate function gives the net change. The definite integral of a rate function gives us the net change in the quantity described by the rate.
Khan Academy
Khan Academy: Worked Example: Problem Involving Definite Integral (Algebraic)
Using definite integral to solve a word problem about the growth in the population of a town.
Wolfram Research
Wolfram Math World: Improper Integrals
Good site from Mathworld.com explaining Improper Integrals. Includes formulas, examples, and links to related sites.
Department of Defense
Do Dea: Ap Calculus
View xplanations and examples using the Fundamental Theorem of Calculus. Great review for the AP Calculus test!
Interactive Mathematics
Interactive Mathematics: The Definite Integral
This demonstration allows you to see the process of finding the definite integral of a function, then put that process to practice in several examples. The definite integral is applied to real world situations such as work and average...