Recall that in Integral Calculus, we can change the variable to of an integral using u-substitution. In other words, we can change from
We would like to do something similar like this with double integrals.
Transformations is about changing from one variable to another. We will first start by transforming regions.
Jacobian of a Transformation
The Jacobian of a transformation & is the following:
It is the determinant of a 2 x 2 matrix.
Change of Variables for a Double Integral
Suppose we want to integrate the function in the region under the transformation & . Then the integral will now become: