Curated OER
Study Guide for the Advanced Placement Calculus AB Examination
Is this going to be on the test? A calculus study guide provides an organized list of important topics and a few examples with answers. The topics include elementary functions, limits, differential calculus, and...
College Board
Seeing Is Believing
Students read about AP calculus online. In this calculus lesson, students learn real life usage for calculus. They read about instructors and their experience teaching and incorporating calculus into the real world.
College Board
Why We Use Theorem In Calculus
Young scholars read an article to explain the reasoning behind theorems. In this calculus lesson, students understand the underlying principles of theorems and how it helps them make sense of the problems. They know why they do what they...
Curated OER
Nine Definite Integrals and Fundamental Theorem Of Calculus Problems
In this definite integral worksheet, student find the value of five definite integrals. Student then explain why a definite integral inequality holds true. Finally, students are given the graph of a functions and asked to...
Curated OER
Introduction to Slope Fields
Students plot slope fields. For this introduction to slope fields lesson, students plot 12 slope fields for given differential equations.
Curated OER
Challenge Sheet 2: Evaluate Functions
In this function worksheet, students evaluate integrals using the fundamental theorem of calculus. They identify the maxima and minima on intervals. This one-page worksheet contains seven problems.
Curated OER
Basic Calculus II: Fundamental Theorem of Calculus
In this fundamental theorem worksheet, students find the antiderivative of a function. This two page worksheet contains five multi-step problems.
Curated OER
Linear Systems
In this linear systems worksheet, students explore the effect of two identical columns in a matrix on the null space of the matrix. They consider the column space of a matrix. Students compare the column space of a matrix to the column...
Mathematics Archives
Math Archives: Visual Calculus: Fundamental Theorem of Calculus 12
This site uses an example to explain the fundamental theorem of calculus. The student can change the problem. At the bottom of the page is a link to a table of elemantary indefinite integrals.
University of St. Andrews (UK)
University of St. Andrews: A History of the Calculus
A site detailing the history of calculus. Many links to informative pages on historical figures. Also links to birthplace maps.
Varsity Tutors
Varsity Tutors: Hotmath: Practice Problems: Integrals
Hotmath provides 24 practice problems dealing with integrals. Each of the practice problems include a step-by-step guide for finding or evaluating the integral.
Mathematics Archives
Math Archives: Visual Calculus: Fundamental Theorem of Calculus
This site visually explores the fundamental theorem of calculus. On-line animation helps the student visualize the process.
Harvey Mudd College
Harvey Mudd College: Fundamental Theorem of Calculus
This site explains the fundamental theorem of calculus with examples.
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.
Richland Community College
Richland Community College: Mathematical Information
This site, which is provided for by the Richland Community College, explains the several mathematical theorems.
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.
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...
Other
Dans Math: Lessons: Calculus (Part 2)
College professor Dan Bach offers a review of the calculus concepts of integrals and vectors. Examples and animated graphs are provided.
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.
Paul Dawkins
Paul's Online Notes: Calculus I: Proof of Various Integral Properties
The tutorial examines proofs of several properties of integrals. Topics discussed are the fundamental theorem of calculus, extreme value theorem, work, and mean value theorem. Class notes, proofs, and examples with detailed solutions are...
Texas Instruments
Texas Instruments: Riemann Sums and the Fundamental Theorem of Calculus
In this activity, students learn and explore how Indefinite integrals are used to find the antiderivative of a function. They also learn that Definite integrals can be used to find the area bounded by a function and the X-axis. From...
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,...
Other
Karl's Calculus Tutor: Integrals
This site provides a detailed overview of intregals, including a focus on the fundamental theorem of calculus to definite and indefinite integrals. Content includes numerous examples and exercises.