Explanation Given: The part of the plane: x + y + z = 1 And the function: f ( x , y , z ) = z Formula Used: ∬ S f ( x , y , z ) d S = ∬ D f ( x , y , z ) d z d x d y … ( 1 ) Calculation: Consider the part of the plane: x + y + z = 1 And the function: f ( x , y , z ) = z Here, z = 1 − x − y g ( x , y ) = 1 − x − y Partial derivative with respect to x , g x = − 1 Partial derivative with respect to y , g y = − 1 Now, d S = 1 + g x 2 + g y 2 d x d y = 1 + ( − 1 ) 2 + ( − 1 ) 2 d x d y = 3 d x d y Since f ( x , y , z ) = z , then f ( x , y , g ( x , y ) ) = g ( x , y ) = 1 − x − y Now, from the equation (1) with the domain 0 ≤ x ≤ 1 , 1 ≤ y ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 17.4, Problem 21E

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To calculate:

$\iint_{S} f (x, y, z) d S$ for the given surface and function.

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Chapter 17.4, Problem 20E

Chapter 17.4, Problem 22E

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

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To calculate:

$\iint_{S} f (x, y, z) d S$ for the given surface and function.

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Chapter 17 Solutions

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

Solution Summary: The author explains how to calculate S f (x, y, and z) d S for the given surface and function.

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

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Chapter 17 Solutions

To calculate:

$\iint_{S} f (x, y, z) d S$ for the given surface and function.