Use Green’s Theorem to prove the change of variables formula for a double
Here R is the region in the xy-plane that corresponds to the region S in the uv-plane under the transformation given by x = g(u, v), y = h(u, v).
[Hint: Note that the left side is A(R) and apply the first part of Equation 5. Convert the line integral over ∂R to a line integral over ∂S and apply Green’s Theorem in the uv-plane.]
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Essential Calculus: Early Transcendentals
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningElements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,