Let S be the surface of the cylinder bounded by z + y = 4 and the planes z = 0 and z = 3, with closed top and open bottom. Let F(z, y, 2) = (z³ + 3zy')i+(zz+arctan 2)j+zz?k. Find F-dS, where S is oriented outward. [Hint: Sis not a closed surface. Also consider the integral of F over the missing bottom of S (with downward orientation) and apply the Divergence Theorem.] Select one: а. 90л b. 18л с. 72т d. 367 e. \(54\pi\)
Let S be the surface of the cylinder bounded by z + y = 4 and the planes z = 0 and z = 3, with closed top and open bottom. Let F(z, y, 2) = (z³ + 3zy')i+(zz+arctan 2)j+zz?k. Find F-dS, where S is oriented outward. [Hint: Sis not a closed surface. Also consider the integral of F over the missing bottom of S (with downward orientation) and apply the Divergence Theorem.] Select one: а. 90л b. 18л с. 72т d. 367 e. \(54\pi\)
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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![Let S be the surface of the cylinder bounded by z +y² = 4 and the planes z = 0 and z= 3, with closed top and open bottom. Let
F(z, y, z) = (x³ + 3zy²) i+ (xz+arctan z) j+ æz² k. Find ||
F. dS, where S is oriented outward.
[Hint: Sis not a closed surface. Also consider the integral of F over the missing bottom of S (with downward orientation) and apply the
Divergence Theorem.]
Select one:
а. 90л
b. 187
с. 72л
d. 367
e. \(54\pi\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50589fea-07bb-4f50-a34c-95e031a700c5%2Fa3edac1a-5c82-41a7-9112-48b149d371d4%2Fhod8ih4_processed.png&w=3840&q=75)
Transcribed Image Text:Let S be the surface of the cylinder bounded by z +y² = 4 and the planes z = 0 and z= 3, with closed top and open bottom. Let
F(z, y, z) = (x³ + 3zy²) i+ (xz+arctan z) j+ æz² k. Find ||
F. dS, where S is oriented outward.
[Hint: Sis not a closed surface. Also consider the integral of F over the missing bottom of S (with downward orientation) and apply the
Divergence Theorem.]
Select one:
а. 90л
b. 187
с. 72л
d. 367
e. \(54\pi\)
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