Evaluate the surface integral Th F⚫ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = -xi - yj + z³k, S is the part of the cone z = √√x² + y² between the planes z = 1 and z = 4 with downward orientation ZA z = √x²+ y² xx z=4

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 32E
Question
Evaluate the surface integral
Th
F⚫ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.
F(x, y, z) = -xi - yj + z³k, S is the part of the cone z = √√x² + y² between the planes z = 1 and z = 4 with downward orientation
ZA
z = √x²+ y²
xx
z=4
Transcribed Image Text:Evaluate the surface integral Th F⚫ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = -xi - yj + z³k, S is the part of the cone z = √√x² + y² between the planes z = 1 and z = 4 with downward orientation ZA z = √x²+ y² xx z=4
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