Consider the vector Field F(x, y, z) = <3x4, 4xz, - 34z+67 25 Consider also the 3-dimensional region D bounded by the surface 5 = SUSZ where S=((x, 4,0): x² +42≤16, the unit disc in the plane z = 0, with boundary circle C={(x,y,0): x²+4²=14 • 52=2(x14, 1-x²-4²): x² + y² ≤14, an upside down paraboloid with the same boundary circlec. let n denote the outward pointing unit normal vector on 5. (Note that ǹ is only piecewise conti- nuous: it is discontinuous along the common. boundary circle C of S, and s₂; but preceuvise Continuity is just fine, as it is in Green's theorem). ①Calculate the surface integral (Ends using a double integral. S₁ Hint: What are the values of F(x, y, z) and of plane z =0? on the ②use previous results to write down the value of the surface integral (F.nds. Sz
Consider the vector Field F(x, y, z) = <3x4, 4xz, - 34z+67 25 Consider also the 3-dimensional region D bounded by the surface 5 = SUSZ where S=((x, 4,0): x² +42≤16, the unit disc in the plane z = 0, with boundary circle C={(x,y,0): x²+4²=14 • 52=2(x14, 1-x²-4²): x² + y² ≤14, an upside down paraboloid with the same boundary circlec. let n denote the outward pointing unit normal vector on 5. (Note that ǹ is only piecewise conti- nuous: it is discontinuous along the common. boundary circle C of S, and s₂; but preceuvise Continuity is just fine, as it is in Green's theorem). ①Calculate the surface integral (Ends using a double integral. S₁ Hint: What are the values of F(x, y, z) and of plane z =0? on the ②use previous results to write down the value of the surface integral (F.nds. Sz
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 10E
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Transcribed Image Text:Consider the vector Field
F(x, y, z) = <3x4, 4xz, - 34z+67
25
Consider also the 3-dimensional region D
bounded by the surface 5 = SUSZ where
S=((x, 4,0): x² +42≤16, the unit disc in the
plane z = 0, with boundary circle C={(x,y,0):
x²+4²=14
•
52=2(x14, 1-x²-4²): x² + y² ≤14, an upside
down paraboloid with the same boundary circlec.
let n denote the outward pointing unit normal
vector on 5. (Note that ǹ is only piecewise conti-
nuous: it is discontinuous along the common.
boundary circle C of S, and s₂; but preceuvise
Continuity is just fine, as it is in Green's theorem).
①Calculate the surface integral (Ends using
a double integral.
S₁
Hint: What are the values of F(x, y, z) and of
plane z =0?
on the
②use previous results to write down the value
of the surface integral (F.nds.
Sz
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