Math Problem Statement

Find ∫∫R-6x+2yx-4ydA, where R is the parallelogram enclosed by the lines -6x+2y=0, -6x+2y=2, x-4y=1, x-4y=6

Solution

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Math Problem Analysis

Mathematical Concepts

Double Integrals
Coordinate Transformation
Jacobian Determinant
Parallelogram Regions

Formulas

Double integral: ∫∫_R f(x, y) dA
Coordinate transformation: u = -6x + 2y, v = x - 4y
Jacobian determinant for variable transformation

Theorems

Change of Variables Theorem for Double Integrals

Suitable Grade Level

Undergraduate Calculus