Find the flow of the field F = ∇(x²ze^y)

a. Once around the ellipse C in which the plane x + y + z = 1 intersects the cylinder x² + z² = 25, clockwise as viewed from the positive y-axis.

b. Along the curved boundary of the helicoid in Exercise 27 from (1, 0, 0) to (1, 0, 2π).

Data from Exercise 27

Find the surface area of the helicoid r(r, θ) = (r cos θ)i + (r sin θ)j + θk, 0 ≤ θ ≤ 2π, 0 ≤ r ≤ 1, in the accompanying figure.

Transcribed Image Text:

(1, 0, 2TT) (1, 0, 0) X N 2TT