4. Evaluate the surface integral SF. F. dS for the vector field F(x, y, z) = xi + yj, where S is the surface with parametric representation r = r(u, v) = 2ui + (u + v)j + (1+u-v)k Give S the positive (outward) orientation. 0≤u≤1, 0≤v≤ 1.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 12E
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4. Evaluate the surface integral
SS
S
for the vector field F(x, y, z) = xi + yj, where S is the surface with parametric representation
r = r(u, v) = 2ui + (u + v)j + (1+u-v)k
F. ds
0 ≤u≤ 1, 0≤v≤ 1.
Give S the positive (outward) orientation.
Transcribed Image Text:4. Evaluate the surface integral SS S for the vector field F(x, y, z) = xi + yj, where S is the surface with parametric representation r = r(u, v) = 2ui + (u + v)j + (1+u-v)k F. ds 0 ≤u≤ 1, 0≤v≤ 1. Give S the positive (outward) orientation.
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