Math Problem Statement

Let C be the positively oriented circle centred at the origine with radius 2. Compute the circulation of the vector F = -yi + xj around a circle C using Green's theorem.

Solution

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Math Problem Analysis

Mathematical Concepts

Vector fields
Green's Theorem
Line integrals
Partial derivatives
Polar coordinates

Formulas

Green's Theorem: \( \oint_C \mathbf{F} \cdot d\mathbf{r} = \iint_D ( \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} ) dA \)

Theorems

Green's Theorem

Suitable Grade Level

Advanced undergraduate level