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Let F(x, y, z) = (xz, yz, z²). (a) Let S be the cylinder a2 + y² = 4, 1 < z < 3, oriented by the outward normal. Find SS;F · dS.

Let F(x, y, z) = (xz, yz, z²). (a) Let S be the cylinder a2 + y² = 4, 1 < z < 3, oriented by the outward normal. Find SS;F · dS.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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it is a multivariable calculus problem.

Let F(x, y, 2) = (xz, yz, z²). (a) Let S be the cylinder x? + y? = 4, 1 < z < 3, oriented by the outward normal. Find ST; F. ds. (b) Suppose that you "close up" the cylinder S in part (a) by adding the disks x? + y² < 4, z = 3, and x2 + y? < 4, z = 1, at the top and bottom, respectively, where the disk at the top is oriented by the upward normal and the one at the bottom is oriented by the downward normal. Let S1 be the resulting surface: cylinder, top, and bottom. Find Sls, F · dS.
Transcribed Image Text:Let F(x, y, 2) = (xz, yz, z²). (a) Let S be the cylinder x? + y? = 4, 1 < z < 3, oriented by the outward normal. Find ST; F. ds. (b) Suppose that you "close up" the cylinder S in part (a) by adding the disks x? + y² < 4, z = 3, and x2 + y? < 4, z = 1, at the top and bottom, respectively, where the disk at the top is oriented by the upward normal and the one at the bottom is oriented by the downward normal. Let S1 be the resulting surface: cylinder, top, and bottom. Find Sls, F · dS.
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