This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the ska Tutorial Exercise Use the Divergence Theorem to calculate the surface integral F. dS; that is, calculate the flux of F across S. F(x, y, z) = 3xy2i + xe'j + z°k, S is the surface of the solid bounded by the cylinder y? + z? = 4. and the planes x = -4 and x = 4 Step 1 If the surface has positive orientation and bounds the simple solid E, then the Divergence Theorem tells us that F.dS = div F dV. For F(x, y, z) = 3xy?i + xe'j + zk we have div F= Step 2 Since S bounds the cylinder y? + z? = 4 between the planes x = -4 and x = 4, we will use cylindrical coordinates, with polar coordinates in the yz-plane. Therefore, y =r cos(0), z=r sin(0), and x = x. We, therefore, have the following. ds = div F dV (*IT cos?(@) + 3 sin (0) )r dx dr de %3D ) dx dr de %3D
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the ska Tutorial Exercise Use the Divergence Theorem to calculate the surface integral F. dS; that is, calculate the flux of F across S. F(x, y, z) = 3xy2i + xe'j + z°k, S is the surface of the solid bounded by the cylinder y? + z? = 4. and the planes x = -4 and x = 4 Step 1 If the surface has positive orientation and bounds the simple solid E, then the Divergence Theorem tells us that F.dS = div F dV. For F(x, y, z) = 3xy?i + xe'j + zk we have div F= Step 2 Since S bounds the cylinder y? + z? = 4 between the planes x = -4 and x = 4, we will use cylindrical coordinates, with polar coordinates in the yz-plane. Therefore, y =r cos(0), z=r sin(0), and x = x. We, therefore, have the following. ds = div F dV (*IT cos?(@) + 3 sin (0) )r dx dr de %3D ) dx dr de %3D
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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