This preview shows page 1. Sign up to view the full content.
Unformatted text preview: the boundary of the region and a clear statement giving the double integral that results from applying Greens Theorem. (Partial credit: For a line integral with P dx + Q dy, start by nding Q xP y . ) 7. (15 points ) Use the Divergence Theorem to nd Z S F n dS when F = x 2 i + (2 y + z ) j + (3 z + x ) k, S is the surface of the cube bounded by x = 0 , x = 1 , y = , y = 2 , z = 1 and z = 3 , and n is the outer normal. 8. (15 points ) Use Stokes Theorem to evaluate the line integral Z C F d r, when F = xz i +3 xy j +3 xy k, and C is the boundary of the part of the plane 3 x + y + z = 3 in the rst octant (oriented counterclockwise when viewed from above)....
View
Full
Document
This note was uploaded on 09/06/2010 for the course MATH 23 taught by Professor Yukich during the Spring '06 term at Lehigh University .
 Spring '06
 YUKICH
 Calculus, Critical Point

Click to edit the document details