Change of Variables (Substitution)
In this lesson on change of variables or substitution, the concept of differentials is introduced in relation to derivatives. The properties of differentials, including linearity, product rule, quotient rule, and chain rule, are covered along with examples. The lesson then delves into indefinite and definite integrals using basic "u-substitutions" and how to compute them. The importance of transforming limits of integration in definite integrals is highlighted through examples.
Differentials. Using basic "u-substitutions" to find indefinite integrals and compute definite integrals.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
- The u-Substitution; Change of Variables - Practice with The u-Substitution; Change of Variables.
- What is change of variables in Calculus?
- What is u-substitution in Calculus?
- What is a differential?
- What are formulas for differentials?
- What is the reverse chain rule?
- How do you do u-substitution?
- How do you find u and du to find an integral?
- How do you find the integral of x/(x - 1)^3?
- How do you find definite integrals using u-substitution?
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Staff Review
Differentials are at the forefront of this lesson. They are used to introduce changing variables in Calculus problems, also called u-substitution. This concept is vital to finding integrals in Calculus. Many example problems where you can see u-substitution in action are shown, so you can see several different scenarios. Both indefinite and definite integrals are shown. -
Vince_II
Definite integral part. The reason why we have U in this case is to find the differential and constant. Never do we replace the U substitution with the previous variable that was replaced.
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