Explanation Given : The surface is over the cylinder x 2 + y 2 = 4 , 1 ≤ z ≤ 5 outward pointing normal. Calculation : Step 1: The surface is parametrized by: Φ ( θ , z ) = ( 2 c o s θ , 2 s i n θ , z ) where the parameter domain is D : 0 ≤ θ ≤ 2 π , 1 ≤ z ≤ 5 For this parametrization, it holds that: T θ × T z = 〈 2 cos θ , 2 sin θ , 0 〉 Step 2: This vector is horizontal and points out of the cylinder. Therefore, n = 〈 2 cos θ , 2 sin θ , 0 〉 Step 3: The dot product F • n is computed as follows: F ( Φ ( θ , z ) ) • n ( θ , z ) = 〈

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 17.5, Problem 12E

To determine

To calculate: The value of $\int \int_{S} F . d s$ for $F = 〈 x, y, e^{z} 〉$ ,over the cylinder $x^{2} + y^{2} = 4, 1 \leq z \leq 5$ outward pointing normal.

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Chapter 17.5, Problem 11E

Chapter 17.5, Problem 13E

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Chapter 17 Solutions

CALCULUS (CLOTH)

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

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Prob. 43E Ch. 17.2 - Prob. 44E Ch. 17.2 - Prob. 45E Ch. 17.2 - Prob. 46E Ch. 17.2 - Prob. 47E Ch. 17.2 - Prob. 48E Ch. 17.2 - Prob. 49E Ch. 17.2 - Prob. 50E Ch. 17.2 - Prob. 51E Ch. 17.2 - Prob. 52E Ch. 17.2 - Prob. 53E Ch. 17.2 - Prob. 54E Ch. 17.2 - Prob. 55E Ch. 17.2 - Prob. 56E Ch. 17.2 - Prob. 57E Ch. 17.2 - Prob. 58E Ch. 17.2 - Prob. 59E Ch. 17.2 - Prob. 60E Ch. 17.2 - Prob. 61E Ch. 17.2 - Prob. 62E Ch. 17.2 - Prob. 63E Ch. 17.2 - Prob. 64E Ch. 17.2 - Prob. 65E Ch. 17.2 - Prob. 66E Ch. 17.2 - Prob. 67E Ch. 17.2 - Prob. 68E Ch. 17.2 - Prob. 69E Ch. 17.2 - Prob. 70E Ch. 17.2 - Prob. 71E Ch. 17.2 - Prob. 72E Ch. 17.2 - Prob. 73E Ch. 17.2 - Prob. 74E Ch. 17.2 - Prob. 75E Ch. 17.3 - Prob. 1PQ Ch. 17.3 - Prob. 2PQ Ch. 17.3 - Prob. 3PQ Ch. 17.3 - Prob. 4PQ Ch. 17.3 - Prob. 1E Ch. 17.3 - Prob. 2E Ch. 17.3 - Prob. 3E Ch. 17.3 - Prob. 4E Ch. 17.3 - Prob. 5E Ch. 17.3 - Prob. 6E Ch. 17.3 - Prob. 7E Ch. 17.3 - Prob. 8E Ch. 17.3 - Prob. 9E Ch. 17.3 - Prob. 10E Ch. 17.3 - Prob. 11E Ch. 17.3 - Prob. 12E Ch. 17.3 - 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The value of ∫ ∫ S F . d s for F = 〈 x , y , e z 〉 ,over the cylinder x 2 + y 2 = 4 , 1 ≤ z ≤ 5 outward pointing normal.

Solution Summary: The author explains how the surface is parametrized by: (, z ) = ( 2 c o

Videos

To calculate: The value of $\int \int_{S} F . d s$ for $F = 〈 x, y, e^{z} 〉$ ,over the cylinder $x^{2} + y^{2} = 4, 1 \leq z \leq 5$ outward pointing normal.

Want to see the full answer?

Chapter 17 Solutions

The value of ∫ ∫ S F . d s for F = 〈 x , y , e z 〉 ,over the cylinder x 2 + y 2 = 4 , 1 ≤ z ≤ 5 outward pointing normal.

Solution Summary: The author explains how the surface is parametrized by: (, z ) = ( 2 c o

Videos

To calculate: The value of ∫∫SF.ds for F=〈x,y,ez〉,over the cylinder x2+y2=4,1≤z≤5 outward pointing normal.

Want to see the full answer?

Chapter 17 Solutions

To calculate: The value of $\int \int_{S} F . d s$ for $F = 〈 x, y, e^{z} 〉$ ,over the cylinder $x^{2} + y^{2} = 4, 1 \leq z \leq 5$ outward pointing normal.