MATH-4600 Homework X Solutions to Graded Problems 1. 7.3 #6 F = (x, y, z) , D = {(x, y, z) : 0 z 9 - x2 - y 2 } Gauss's Theorem:
S
F dS =
V
FdV
(a)
- (s, t) = (s cos(t), s sin(t), 0) x F dS =
S 2 3 Sbottom
F dS +
Stop
F dS
F dS =
S 2
MATH-4600 Homework VII Solutions to Graded Problems 1. 6.2 #1 F (x, y) = -x2 y, xy 2 , D = x2 + y 2 4 (a) C1 : x = 4 - t2 , y = t, -2 t 2 C2 : x = - 4 - t2 , y = t, -2 t 2 M dx + N dy =
D D
-x2 ydx + xy 2 dy -x2 ydx + xy 2 dy
C2
=
C1
-x2 ydx