MAC-2313 Chapter 8: Study Guide 107 (Line Integrals in R3)

Proof Let , where M and N have continuous first partial derivatives in a simply connected region R. Prove that if C is simple, smooth, and closed, and then .

Let C be a simple closed smooth curve that lies in the plane x + y + z = 1. Show that the line integral (zdx -2xdy + 3ydz) depends only on the area of the region enclosed by C and not on the shape or location.