Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: THEend8_
ASSIGNMENT 10
Problem 1 (12 marks)
(a) (7 marks) Evaluate the integral
∮
C
F · n ds, where F(x, y) = 〈x+ y, x2 + y2〉, C is the
curve x
2
4
+ y
2
9
= 1 (counterclockwise oriented), and n is the outward unit normal vector to
the curve C.
(b) (5 marks) Use the divergence theorem to solve the problem (a) above.
Problem 2 (8 marks)
Evaluate the integral
∫∫
S
x2(z2 + y2) dS, where S is a part of the cylinder x2 + y2 = 4,
2 < z < 5.
Problem 3 (10 marks) Use Stokes’ theorem (surface integral) to evaluate the integral∮
C
F · dr, where F(x, y, z) = 〈xy + z2, x+ z, xy2 + z〉 and C is the intersection curve of the
sphere x2 + y2 + z2 = 10 and the plane z = 2, counterclockwise oriented when it is viewed
from the positive z-axis.