Chapter 17.4, Problem 15E

Suppose C is the boundary of region R = {(x, y):x² ≤ y ≤ 1},oriented counter clockwise (see figure); F = $\langle 1,x\rangle$.

a. Compute the two-dimensional curl of F and determine whether F is irrotational.

b. Find parameterizations r₁(t) and r₂(t) for C₁ and C_2, respectively.

c. Evaluate both e line integral and the double integral in the circulation form of Green’s Theorem and check for consistency.

d. Compute the two-dimensional divergence of F and use the flux form of Green’s Theorem to explain why the outward flux is 0.