Unformatted text preview: the boundary of the region and a clear statement giving the double integral that results from applying Green’s Theorem. (Partial credit: For a line integral with P dx + Q dy, start by ﬁnding Q xP y . ) 7. (15 points ) Use the Divergence Theorem to ﬁnd 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 ﬁrst octant (oriented counterclockwise when viewed from above)....
View
Full Document
 Spring '06
 YUKICH
 Calculus, Critical Point, Vector Calculus, Vector field, Stokes' theorem

Click to edit the document details