Explanation Given information : y = 4 − z 2 , 0 ≤ x ≤ z ≤ 2 ; f ( x , y , z ) = 3 Formula used: The surface integral over a graph y = g ( x , z ) : ∬ S f ( x , y , z ) d S = ∬ D f ( x , g ( x , z ) , z ) 1 + g x 2 + g y 2 d x d z Calculation: y = 4 − z 2 (Given) y = g ( x , z ) = 4 − z 2 g x = 0 g z = − 2 z Then 1 + g x 2 + g y 2 = 1 + 4 z 2 and f ( x , y , z ) = 3 . ∬ S f ( x , y , z ) d S = ∬ D f ( x , g ( x , z ) , z ) 1 + g x 2 + g y 2 d x d z = ∬ D 3 1 + 4 z 2 d x d

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17.4, Problem 16E

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To calculate: ∬Sf(x,y,z)dS for the given surface and function.

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Chapter 17.4, Problem 15E

Chapter 17.4, Problem 17E

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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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∬ S f ( x , y , z ) d S for the given surface and function.

Solution Summary: The author explains the formula used to calculate the surface integral over a graph: y=g(x,z)=4-z2.

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To calculate: ∬Sf(x,y,z)dS for the given surface and function.

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Chapter 17 Solutions