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Series: Calculus: Basics of Integration

About this Series

  • Lessons: 14
  • Total Time: 2h 53m
  • Use: Watch Online & Download
  • Access Period: Unlimited
  • Created At: 07/29/2009
  • Last Updated At: 07/20/2010

In this 14-lesson series, we'll learn about antidifferentiation, or integration, and the Fundamental Theorem of Calculus. Integration is the process by which you can reverse differentiation. Just as we learned several rules to help us find the derivative of different functions, we'll learn several rules to help us find the integral of different functions. In most cases, untangling the rules of differentiation will lead us to a rule of integration. These rules will help us integrate functions that involve trigonometric and exponential expressions functions. The most common integration technique is called integration by substitution. It is arrived at by untangling the chain rule that we learned in our lessons on differentiation.

Where we learned differentiation in Calculus I and it helped us to answer the question of how to find an instantaneous rate of change, integration will be the focus of Calculus II and it will help us to answer the question of how to find the area of unusual figures. We'll start exploring this notion in this series. The fundamental theorem of calculus provides a means of evaluating definite integrals. Definite integrals have prescribed enpoints and are the integrals that are associated with calculating areas under curves. We'll learn more about the fundamental theorem of Calculus and how it enables us to find the area between a curve and the x-axis by working through several integration problems using it to find this area.

Taught by Professor Edward Burger, this series comes from a comprehensive Calculus course. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers limits, derivatives, implicit differentiation, integration or antidifferentiation, L'Hopital's Rule, functions and their inverses, improper integrals, integral calculus, differential calculus, sequences, series, differential equations, parametric equations, polar coordinates, vector calculus and a variety of other AP Calculus, College Calculus and Calculus II topics.

About this Author

2174 lessons

Founded in 1997, Thinkwell has succeeded in creating "next-generation" textbooks that help students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technology-based textbooks. For more information about Thinkwell, please visit or visit Thinkwell's Video Lesson Store at

Thinkwell lessons feature a star-studded cast of outstanding university professors: Edward Burger (Pre-Algebra through...

Lessons Included

Definitely the best on definite integrals pract...
~ Jennifer68

A great combination of "DIY" problems! Practice and use U-substitution, breaking terms apart and intuition! Exactly the kind of review I needed before my test!

Professor Burger, Calculus
~ Benjamin9

If you don't get it the first time, or the second or the third or the fourth - fear not. Professor Burger is always interesting and fun to listen to. And eventually you'll get it!

You have reached me!
~ greenshoes

excellent - getting an A in calculus (because I watch these videos) I may be speaking for myself but I almost literally never go to class and yet feel so motivated by these videos that I often spend time outside of class and outside of these videos, thinking about about calculus! May sound far fetched but watch Prof Burgers videos and I bet you find yourself doing the same thing! Thanks Professor for the excellent instruction!

Great overview of derivatives!
~ brittanie

In school it was really hard for me to learn how to find integrals or derivatives. Trig is hard! Especially when you're working with derivatives and trig functions. I like Professor Burger's teaching style. He's really easy to follow.

Good lesson
~ nachan

Professor Burger helps you find a formula to find the antiderivative. I found this lesson to be a little bit more confusing but I thin it might be because explaining the antiderivatives of powers of x are more difficult than most math problems. He always does a great job explaining the meaning of each term and gives great formulas to answer the problem.

Below are the descriptions for each of the lessons included in the series:

Supplementary Files: