Substitution of the variables in double integration

Description
How the variables in a double integral can be substituted by other variables, this is explained through examples in this video lecture. The double integral of a function of two variables can be integrated easily using the substitution method. How can both the variables be substituted independently, this is shown in examples.
Prof. Denis Auroux, Maths, 18.02 Multivariable Calculus, Fall 2007: 18: Change of Variables, Massachusetts Institute of Technology: MIT OpenCourseWare),http://ocw.mit.edu (Accessed September,22,2011). License: Creative Commons BY-NC-SA:http://ocw.mit.edu/terms/#cc