Suppose that S is a surface in R³ with a parametrization O whose domain D is the square shown in the figure. The values of a function f, a vector field F, and the normal vector N = T, × T, at (P) are given for the four sampl points in D in the table. Point P in D f F N A 4 (2, 8, 4) (1, 1, 1) B 1 (1,1,7) (1, 1,0) C 2 (3, 3, –3) (1,0, – 1) D 7 (0, 1, 8) (2, 1,0) Estimate the surface integrals of f and F over S. (Use decimal notation. Round your answers to three decimal places.)
Suppose that S is a surface in R³ with a parametrization O whose domain D is the square shown in the figure. The values of a function f, a vector field F, and the normal vector N = T, × T, at (P) are given for the four sampl points in D in the table. Point P in D f F N A 4 (2, 8, 4) (1, 1, 1) B 1 (1,1,7) (1, 1,0) C 2 (3, 3, –3) (1,0, – 1) D 7 (0, 1, 8) (2, 1,0) Estimate the surface integrals of f and F over S. (Use decimal notation. Round your answers to three decimal places.)
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 O whose domain D is the square shown in the figure.
The values of a function f, a vector field F, and the normal vector N = T, x T, at 0(P) are given for the four sample
points in D in the table.
Point P in D
f
F
N
A
4
(2, 8, 4)
(1,1, 1)
B
1
(1,1,7)
(1, 1,0)
C
2
(3, 3, –3)
(1,0, – 1)
D
7
(0, 1,8)
(2, 1,0)
Estimate the surface integrals of f and F over S.
(Use decimal notation. Round your answers to three decimal places.)
/| f(x, y, z) dS
F. dS =
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