Domain of Science
Calculus, What Is It Good For?
Explore the meaning of differentiation and integration. A video lesson describes in detail what differentiating and integrating an equation means using the momentum and kinetic energy formulas. Progressing from a linear to a quadratic...
3Blue1Brown
Integration and the Fundamental Theorem of Calculus | Essence of Calculus, Chapter 8
Integrate a great resource into your lesson plans. The eighth video in an 11-part series explains integration and the relationship between derivatives and integrals. The relationship between a car's velocity and its travel distance...
3Blue1Brown
Essence of Calculus, Chapter 1
Dive into the essence of calculus. The first installment of an 11-part playlist introduces the video series by looking at the area of a circle and the area under curves. The narrator explains how to look at calculus as taking a hard...
3Blue1Brown
What Does Area Have to Do with Slope? | Essence of Calculus, Chapter 9
It seems like area and slope wouldn't have any connection. Here is a video that explains how to find the average value of a function over an interval. It connects the area under a curve to the slope of the antiderivative curve.
Educator.com
Separation of Variables and Initial Value Problem
Ap Calculus classes learn how to solve a differential equation by getting like variables together with a video that presents an example of how to solve a differential equation by using the method of separation of variables. The...
Educator.com
Trigonometric Integrals
Present examples of trigonometric integrals with a video that shows an example of determining a trigonometric integral. The AP Calculus example shows that many of the trigonometric integrals require manipulation and using trigonometric...
Educator.com
Integration by Parts
Class members view how to derive the formula to integrate by parts with a video that uses the Product Rule from the beginning of AP Calculus to derive the rule to integrate products. The resource shows the...
Educator.com
Volumes: Solids That are Not Solid of Revolution
Viewers learn how to calculate the volume when the cross section is not a circle by using the same principle as if it was a circle. The video goes through an example of finding the volume of a figure where the cross sections are squares...
Educator.com
Solving Integrals Using Substitution
The concept of solving integrals by substitution with trigonometric functions is modeled by a video designed for AP Calculus classes. The narrator works an example problem using substitution and shows that careful substitution...
Educator.com
Properties of the Definite Integral
What are the properties that can be associated with the definite integral? The AP Calculus video lists nine properties of the definite integral and provides explanations of why the properties hold for integrals in language that is...
Educator.com
Finding The Area Under a Curve Using Rectangles
Here's an AP Calculus video that provides a discussion on determining an approximate for the area under a curve by calculating the sum of areas of rectangles that is smaller than the area and by finding the sum of areas of...
Educator.com
Integration by Partial Fractions
Demonstrate a complex integration by using partial fractions with an AP Calculus resource that works an example of integrating a rational function. The function's denominator has linear factors with one of them repeated.
Educator.com
Average Value of a Function
Viewers learn how to find the average of a variable density with a video made for AP Calculus. The presenter applies the formula to find the average value of a function with an example that provides a density function for a rod. The...
Educator.com
Volumes by Cylindrical Shells
Shells sometimes work better than washers. The AP Calculus video presents an example of finding the volume of a rotational solid by using the shell method. The method uses the integral of the lateral surface area of a cylinder as...
Educator.com
Volumes by Washers
Here's an AP Calculus resource that works an example problem of finding the volume where the cross sections of a solid are washer shaped. In the example the axis of rotation is vertical, creating horizontal washers.
Educator.com
Areas Between Curves
There are times that it is necessary to add areas to find the area between the curves. The video for AP Calculus presents how to find the area between curves by subtracting the area under the lower curve from the area under the upper...
Educator.com
The Second Fundamental Theorem of Calculus
How many fundamental theorems are there? The Second Fundamental Theorem of Calculus is also known as the second part of the Fundamental Theorem of Calculus. Here's a video that introduces the theorem as the method to...
Educator.com
Volumes by Slicing
Find the volume of a rotational solid by integrating the area of a slice. The AP Calculus resource works through an example of finding the volume of a solid created by rotating a function about the x-axis. The presentation breaks the...
Educator.com
Antiderivatives: Finding Position and Velocity
This AP Calculus resource works through an example that shows how to find the velocity function and the position function given acceleration. It concludes by covering how to use them to solve problems.
Crash Course
Derivatives
Physics and math are closely associated in the science community. High schoolers use information in the video to determine how derivatives and calculus help them understand our local environment. They complete problems that relate to...
Crash Course
Integrals
How can you best teach your class to gauge distance when several other key factors are already in place? Pupils learn to use integrals to determine distance from a problem that includes multiple other key points of information....
Math Meeting
Integrals - U Substitution (Part 1)
Want to create more independent learning environment? The provided video gives a clear explanation of integration using U-substitution. Use is as a teaching tool or as supplemental material for your unit on limits.
Khan Academy
Khan Academy: U Substitution: (2^Ln X)/x Antiderivative Example
This video tutorial provides an example of using u-substitution to find an indefinite integral.
Khan Academy
Khan Academy: Calculus Ab Example Questions: 2011 Calculus Ab Free Response #4 A
Taking derivatives and integrals of strangely defined functions.