Explanation Given: F ( x , y , z ) = 〈 y , x , e x z 〉 , x 2 + y 2 = 9 , x ≥ 0 , y ≥ 0 , − 3 ≤ z ≤ 3 with outward-pointing normal. Formula used: ∬ S F . d S = ∬ S F . N d S Calculation: Parametrization of given surface is S ( θ , z ) = ( 3 cos θ , 3 sin θ , z ) , 0 ≤ θ ≤ π 2 , − 3 ≤ z ≤ 3 S θ ( θ , z ) = ( − 3 sin θ , 3 cos θ , 0 ) S z ( θ , z ) = ( 0 , 0 , 1 ) Thus, N= S θ × S z = | i j k − 3 sin θ 3 cos θ 0 0 0 1 | = i ( 3 cos θ ) + j ( 3 sin θ ) + k ( 0 ) = 〈 3 cos θ , 3 sin θ , 0 〉 Hence, the normal vector N = 〈 3 cos θ , 3 sin θ , 0 〉 Therefore, ∬ S F ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 17, Problem 52CRE

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To compute $\iint_{S} F . d S$ .

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Chapter 17, Problem 51CRE

Chapter 17, Problem 53CRE

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Calculate (1), where (2) and γ is the intersection of the surface z = y2 with the plane x + z = 1, oriented in the directionof the growth of y. Answer is 2

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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To compute ∬ S F . d S .

Solution Summary: The author explains the formula used to compute S F. d S.

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To compute $\iint_{S} F . d S$ .

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Chapter 17 Solutions

To compute ∬ S F . d S .

Solution Summary: The author explains the formula used to compute S F. d S.

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To compute ∬SF.dS.

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Chapter 17 Solutions

To compute $\iint_{S} F . d S$ .