Activity 13.9.2

For each of the curves described below, find the circulation of the given vector field around the curve. Do this both by calculating the line integral directly as well as by calculating the double integral from Green's Theorem.

1. The curve $C_1$ is the circle of radius $3$ centered at the point $(2,1)$ (oriented counterclockwise) and the vector field is $\vF = \langle y^2, 5x+2xy\rangle$.

2. The curve $C_2$ is the triangle with vertices $(0,0)$, $(3,0)$, and $(3,3)$ (oriented counterclockwise) and the vector field is $\vG = \langle y^2, 3xy\rangle$.