For the following two vector fields F, compute the Circulation of F along the curve C and the outward Flux
of F across the curve C. Note, the given curve C is positively oriented (i.e., counter-clockwise direction and
outward-pointing unit normal vector). Then, check the result with direct computations (that is, using directly
the definition of flow and flux).
(a) (4pts) F = xy^2
i + x^
2y j and C is the top half-circle y =
√
4 − x
2 ≥ 0 together with the portion on the
horizontal axis −2 ≤ x ≤ 2.
(b) (4pts) F = e^
y
i + 5 sin x j and C is the triangle with vertices (0, 0), (3, 0), and (0, 6)
