# Lecture 18: Change of variables

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Lesson Summary:

In this lesson, you will learn about the change of variables method and how it can simplify difficult integrals. The instructor first walks through a simple example where the area of an ellipse is calculated using a change of variables to rescale x and y coordinates. Then, the general problem of finding the scaling factor for a more complicated change of variables is discussed. The instructor explains how to find the scaling factor and highlights the importance of the determinant of the transformation in scaling areas. Overall, this lesson provides a useful tool for tackling difficult integrals.

Lesson Description:

Learn about the change of variables method for difficult integral calculations.

Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 21, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.

• How do you change variables in double integrals?
• How do you use u and v substitution with a double integral?
• How do you find the area scaling factor when changing from dxdy to dudv?
• What is the Jacobian of a change of variables and how do you find it?
• How do you find the double integral of x^2y dxdy from 0 to 1 for x and y using a change of variables?
• How do you find the new bounds when you change variables in a double integral?
• #### Staff Review

• Currently 4.0/5 Stars.
Change of variables in double integrals is discussed. This can really simplify a double integral, but it has to be done carefully. This process is described very well with some great example problems. The Jacobian is also discussed and examples are shown. The strength of this lecture is its useful example problems that are computed.
• #### gtg789w

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Very good video. Excellent examples with ample explanation.
• #### yoleven

• Currently 5.0/5 Stars.
Very clear and thorough explanations.