Math Problem Statement

  1. Evaluate [Sxy A dx dy, where A is the region common to the circles x² + y = x, x² + y² = y.

Solution

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Math Problem Analysis

Mathematical Concepts

Multivariable Calculus
Double Integrals
Geometry of Curves

Formulas

Double integral: ∫∫(xy) dx dy
Equation of a parabola: y = x - x²
Equation of a circle: x² + (y - 1/2)² = 1/4

Theorems

Green's Theorem (optional for deeper analysis of the region)
Geometric methods for finding intersections of curves

Suitable Grade Level

Undergraduate Level (Calculus II or III)