This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: (25) Let v F = a x,y,z A , and consider the portion D of the cylinder x 2 + y 2 < 1 which lies above the xyplane and inside the sphere x 2 + y 2 + z 2 = 2. a) (15) Calculate the Fux of v F out of D by directly evaluating surface integrals. (do not use the divergence theorem) b) (10) Use the result of part (a) to ±nd the volume of D . (Justify your answer carefully). Problem 5. (25) Consider the surface S given by the graph z = x 2 − y 2 over the unit disk x 2 + y 2 < 1. Let C be the boundary of S oriented counterclockwise when viewed from above. a) (10) ²ind the work done by v F = xy ˆ k around C by directly evaluating a line integral. b) (15) Verify your answer by applying Stokes’ theorem....
View
Full Document
 Fall '08
 Auroux
 Vector Calculus, sphere x2, cylinder x2, Stokes' theorem

Click to edit the document details