Change of Variables in Multiple Integrals | Example with Double Integral Transformation
In this video, I solve a double integral using a change of variables to simplify the region and the integrand. We start by transforming the original integral of the function (x – 3y) over a triangular region with given vertices using a transformation of variables, x = 2u + v and y = u + 2v. By applying the transformation and calculating the Jacobian determinant, we convert the integral into a simpler form, and then solve it using the new variables u and v. This step-by-step example will help you understand how to use a change of variables in multiple integrals, specifically in the context of double integrals.
What You Will Learn:
How to set up and evaluate a double integral using a change of variables.
How to apply a transformation of variables in a multiple integral.
How to calculate the Jacobian determinant for a transformation.
How to simplify the limits of integration using a geometric interpretation of the region.
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