Curated OER
Lights in the Deep
Students describe, compare, and contrast bioluminescence, fluorescence, phosphorescence, and chemiluminescence. They explain the role of three major components of bioluminescent systems. They ex
Curated OER
Patterns
Fifth graders explore patterns. In groups, 5th graders participate in a "Pasta Pattern" activity. Given a bag of pasta, classmates sort pasta by shapes. They use pasta pieces to model different patterns. Students complete a bean...
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.
Stefan Warner and Steven R. Costenoble
Finite Mathematics & Applied Calculus: The Definite Integral: Numerical and Graphical Approaches
Students learn how to evaluate the definite integral using numerical and graphical approaches. Topics examined are Riemann sums and the definite integral. The tutorial explores the calculus concepts through notes and examples. Review...
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.
Other
Metal: Integration [Pdf]
The resource is a lesson guide that teaches the mathematical concept of integration. The guide brings alive the topic of integration and its applications. Topics include definite integrals, integration with exponential functions, and...
University of British Columbia
Ubc: The Definite Integral
This site is a tutorial on the definite integral.
Other
Xetc: Integral Definida
The concept of definite Integral is presented in an interactive manner. The explanation is detailed and step by step. At the end you will find exercises whose solutions are available.
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.
Other
Jfm: The Definition of Riemann Definite Integral
This site introduces Riemann definite integral on the closed interval of real. If you are interested in exploring definite integrals, this site may interest you.
Analyze Math
Analyze Math: Definition of Definite Integrals Riemann Sums
The applet examines the definition of the definite integral.
Texas Instruments
Texas Instruments: Planting & Harvesting an Application of the Definite
In this Derive activity, students apply the concept of definite integration and decide when a farmer should plant and harvest a crop of clover.
Stefan Warner and Steven R. Costenoble
Finite Mathematics & Applied Calculus: The Definite Integral: Algebraic Approach and the Ftc
Students learn how to evaluate the definite integral using an algebraic approach and the Fundamental Theorem of Calculus. Topics examined are the antiderivative, substitution technique, and marginal cost. The tutorial explores the...
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...
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...
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...
Texas Instruments
Texas Instruments: Accumulation Functions
In this activity, students examine functions defined by a definite integral. They create tables and graphs for integration functions. They understand the foundation of the Fundamental Theorem of Calculus.
Ministry of Education and Universities of the Region of Murcia (Spain)
Ministerio De Educacion Y Ciencia: La Integral Definida Y La Function Area
In Spanish. This interactive unit visually presents the concept of the definite integral and its properties.
Khan Academy
Khan Academy: Analyzing Problems Involving Definite Integrals
Given a word problem that involves rates and accumulation, find the appropriate expression for solving the problem.
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.
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