About this Series
 Lessons: 2
 Total Time: 0h 23m
 Use: Watch Online & Download
 Access Period: Unlimited
 Created At: 06/23/2009
 Last Updated At: 07/20/2010
In this two part series, you will learn to do integration by substitution, which is a fancy way of saying that we'll learn to solve integration problems by undoing the chain rule, which is a fundamental technique we should know from differentiation. Since integration (antidifferentiation) and differentiation are inverse operations, we see many of the same patterns in integrals that we do with derivatives. Professor Burger will show you how to recognize integral problems that you may be able to solve by untangling the chain rule.
Part two will teach you how to do integration of polynomials using substitution. Before digging in on substitution in antidifferentiation, Professor Burger will review notation associated with differentiation and antidifferentation (with respect to x). Next, he will move on to teach you integration by substitution, a technique that is helpful for finding the antiderivative of a composite function. While running through the chain rule backwards, he will highlight several rules and properties of antidifferentiation; for instance, the integral of a product is not necessarily equal to the product of the integrals. He also gives us advice on what expressions to select and replace with a constant when using substitution as a method of integration. To illustrate all of this, you will find the integral of 42x(x^2+4)^20 dx as well as the integral of this expression that contains radicals 2x^2*(5+x^3)^(1/2)dx.
This series is a great review for a CLEP test, midterm, final exam, summer school, or personal growth!
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Calculus. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/calculus. The full course covers limits, derivatives, implicit differentiation, integration or antidifferentiation, L'Hôpital'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.
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 Thinkwell
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Thinkwell lessons feature a starstudded cast of outstanding university professors: Edward Burger (PreAlgebra through...
Lessons Included
Below are the descriptions for each of the lessons included in the series:

Calculus: Undoing the Chain Rule
In this video, you will learn to do integration by substitution, which is a fancy way of saying that we'll learn to solve integration problems by undoing the chain rule, which is a fundamental technique we should know from differentiation. Since integration (antidifferentiation) and differentiation are inverse operations, we see many of the same patterns in integrals that we do with derivatives. Professor Burger will show you how to recognize integral problems that you may be able to solve by untangling the chain rule.
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/calculus. The full course covers limits, derivatives, implicit differentiation, integration or antidifferentiation, L'Hôpital'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.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

Calculus: Integrating Polynomials by Substitution
This lesson will teach you how to do integration of polynomials using substitution. Before digging in on substitution in antidifferentiation, Professor Burger will review notation associated with differentiation and antidifferentation (with respect to x). Next, he will move on to teach you integration by substitution, a technique that is helpful for finding the antiderivative of a composite function. While running through the chain rule backwards, he will highlight several rules and properties of antidifferentiation; for instance, the integral of a product is not necessarily equal to the product of the integrals. He also gives us advice on what expressions to select and replace with a constant when using substitution as a method of integration. To illustrate all of this, you will find the integral of 42x(x^2+4)^20 dx as well as the integral of this expression that contains radicals 2x^2*(5+x^3)^(1/2)dx.
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/calculus. The full course covers limits, derivatives, implicit differentiation, integration or antidifferentiation, L'Hôpital'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.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
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