ppose that S is a surface in R³ with a parametrization whose domain D is the square shown in the figure. Å ċ 5 B b e values of a function f, a vector field F, and the normal vector N = Tux T, at D(P) are given for the four sample points in in the table. Point P in D F.dS≈ A B C 1 D f(x, y, z) ds≈ f 3 1 2 8 F (2,2,4) (1, 1,7) (3,3,-3) (0, 1,8) N (1,1,1) (1, 1,0) imate the surface integrals of f and F over S. se decimal notation. Round your answers to three decimal places.) (1, 0, -1) (2, 1,0)
ppose that S is a surface in R³ with a parametrization whose domain D is the square shown in the figure. Å ċ 5 B b e values of a function f, a vector field F, and the normal vector N = Tux T, at D(P) are given for the four sample points in in the table. Point P in D F.dS≈ A B C 1 D f(x, y, z) ds≈ f 3 1 2 8 F (2,2,4) (1, 1,7) (3,3,-3) (0, 1,8) N (1,1,1) (1, 1,0) imate the surface integrals of f and F over S. se decimal notation. Round your answers to three decimal places.) (1, 0, -1) (2, 1,0)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose that S is a surface in R³ with a parametrization whose domain D is the square shown in the figure.
1
Å
ċ
F
B
The values of a function f, a vector field F, and the normal vector N = Tu X T, at (P) are given for the four sample points in
D in the table.
Ď
F. dS
Point P in D
A
B
C
D
f(x, y, z) ds ≈
f
3
1
2
8
F
(2,2,4)
(1, 1,7)
(3,3,-3)
(0, 1,8)
N
(1,1,1)
(1, 1,0)
Estimate the surface integrals of f and F over S.
(Use decimal notation. Round your answers to three decimal places.)
(1, 0, -1)
(2, 1,0)
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