Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Elliptic Regions
Coordinate Transformation
Jacobian Determinant
Multivariable Calculus
Integral Transformation

Formulas

Jacobian: J(u,v) = |∂(x,y)/∂(u,v)|
Ellipse equation: (x^2)/4 + (y^2)/9 = 1
Variable transformations: x = 2u, y = 3v
Integral transformation: ∫∫_D y dA = ∫∫_S f(u,v) du dv

Theorems

Jacobian determinant for coordinate transformation
Area transformation in multivariable calculus

Suitable Grade Level

Undergraduate Calculus