New York State Education Department
TASC Transition Curriculum: Workshop 13
The six instructional shifts in this workshop definitely move math and science teachers' understanding of instruction. The workshop, 13th out of a series of 15, asks participants to examine sample tests and to look at how the six...
University of Vienna (Austria)
University of Vienna: Definite Integrals Sine Function
A series of trigonometric definite integrals are presented, along with three answers for each question (one correct, two incorrect). After choosing all answers, the site returns a score to judge understanding of definite integrals of the...
University of Vienna (Austria)
University of Vienna: Definite Integrals Cosine Function
A series of trigonometric definite integrals are presented, along with three answers for each question (one correct, two incorrect). After choosing all answers, the site returns a score to judge understanding of definite integrals of the...
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.
Khan Academy
Khan Academy: Analyzing Problems Involving Definite Integrals
The interpretation of definite integrals as accumulation of quantities can be used to solve various real-world word problems.
University of British Columbia
Ubc: The Definite Integral
This site is a tutorial on the definite integral.
Analyze Math
Analyze Math: Definition of Definite Integrals Riemann Sums
The applet examines the definition of the definite integral.
Paul Dawkins
Paul's Online Notes: Calculus I: Integrals
The tutorial investigates integrals. Topics discussed are indefinite integrals, area problems, definite integrals, and the substitution rule. Class notes, definitions, and examples with detailed solutions are included. The class notes...
Analyze Math
Analyze Math: Find Area Under Curve
Scholars examine how to find the area under and between curves using definite integrals. The tutorial consists of practice exercises and examples with solutions.
Wolfram Research
Wolfram Math World: Leibniz Integral Rule
This page discusses the Leibniz Integral Rule, which concerns "the differentiation of a definite integral whose limits are functions of the differential variable."
Khan Academy
Khan Academy: Worked Example Motion Problems With Definite Integrals
Remember, anti derivative of acceleration with respect to time is velocity and anti derivative of velocity with respect to time is distance where acceleration, velocity, distance are all functions of t, the time. This concept is very...
Interactive Mathematics
Interactive Mathematics: Integration
This lesson puts integration to work. Lessons include integral, derivatives, antiderivatives, and indefinite integrals. The Trapezoidal and Simpson's Rules are highlighted. The examples are enhanced using Live, Math and Scientific...
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.
Khan Academy
Khan Academy: Area Between Curves
By integrating the difference of two functions, you can find the area between them. Created by Sal Khan.
Wolfram Research
Wolfram Math World: Fundamental Theorem of Calculus
This MathWorld site offers an explanation of the fundamental theorem of calculus includes links to other relevant information.
Paul Dawkins
Paul's Online Notes: Calculus I: Applications of Integrals
The tutorial investigates applications of integrals. Topics discussed are average function value, area between two curves, volumes of solids of revolution, and work. Class notes, definitions, and examples with detailed solutions are...
Paul Dawkins
Paul's Online Notes: Calculus Ii: Applications of Integrals
The resource examines applications of integration. Topics investigated are arc length, surface area, center of mass, hydrostatic pressure, and probability density functions. Class notes, definitions, and examples with detailed solutions...
Scholastic
Scholastic Instructor: Origami Math
Have you ever tried origami? This Japanese form of paper folding is the basis of this math lesson plan. Students will have an opportunity to integrate their creative side with their math skills.
Mathematics Archives
Math Archives: Visual Calculus: Antiderivatives/average Value of a Function
This site has the definition of average of a function by using integrals. The site also contains the proof of the mean value theorem which may be viewed one step at a time. There are links to related exercises whose answer is shown one...
BBC
Bbc: Integration
Several topics of integration are presented, including definite and indefinite integrals, trig integration, and area under curves. Examples and a practice test are included.
Math Open Reference
Math Open Reference: Riemann Sums
A complete reference guide to Riemann Sums. It provides definitions, examples, and an interactive activity that enhances further explanation. Includes links to related topics.
Math Open Reference
Math Open Reference: Separation of Variables
Learn about the separation of variables with this helpful reference tool. Provides a detailed definition, examples, and an interactive activity that enhance further explanation. Includes links to related topics.
University of Arizona
Math Lesson: Calculating Parts Per Million: Do We Have a Problem Here?
Twelfth graders test solutions to determine the parts per million and whether a lake is contaminated.