Explanation Given info: f ( x , y , z ) = ( x − y ) ( y − z ) [ 0 , 1 ] × [ 0 , 3 ] × [ 0 , 3 ] Concept used: Fubini’s theormem for triple product if f is continuous on the rectangular box = B [ a × b ] × [ c , d ] × [ r , s ] ∭ B f ( x , y , z ) d v = ∫ r s ∫ c d ∫ a d f ( x , y , z ) d x d y d z Calculation: f ( x , y , z ) = ( x − y ) ( y − z ) [ 0 , 1 ] × [ 0 , 3 ] × [ 0 , 3 ] ∭ B f ( x , y , z ) d x d z d y ( putting the value of limit and function ) = ∫ 0 3 ∫ 0 3 ∫ 0 1 ( x − y ) ( y − z ) d x d z d y ( simplifying the expression inside the integration ) = ∫ 0 1 ∫ 0 3 ∫ 0 3 ( x y − x z − y 2 + y z ) d z d y d x = ∫ 0 1 ∫ 0 3 [ ∫ 0 3 ( x y − x z − y 2 + y z ) ] d y d x ( rewrite the expression ) Integrate w ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.3, Problem 5E

To determine

Evaluate $\underset{B}{∭} f (x, y, z) d v$ for the specified function $f$ and box $B .$

$f (x, y, z) = (x - y) (y - z), [0, 1] \times [0, 3] \times [0, 3]$

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Chapter 16.3, Problem 4E

Chapter 16.3, Problem 6E

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Chapter 16 Solutions

CALCULUS (CLOTH)

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

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Evaluate ∭ B f ( x , y , z ) d v for the specified function f and box B . f ( x , y , z ) = ( x − y ) ( y − z ) , [ 0 , 1 ] × [ 0 , 3 ] × [ 0 , 3 ]

Solution Summary: The author explains Fubini's theormem for triple product if f is continuous on the rectangular box = B.

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Evaluate $\underset{B}{∭} f (x, y, z) d v$ for the specified function $f$ and box $B .$

$f (x, y, z) = (x - y) (y - z), [0, 1] \times [0, 3] \times [0, 3]$

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Chapter 16 Solutions

Evaluate ∭ B f ( x , y , z ) d v for the specified function f and box B . f ( x , y , z ) = ( x − y ) ( y − z ) , [ 0 , 1 ] × [ 0 , 3 ] × [ 0 , 3 ]

Solution Summary: The author explains Fubini's theormem for triple product if f is continuous on the rectangular box = B.

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Evaluate ∭Bf(x,y,z)dv for the specified function f and box B. f(x,y,z)=(x−y)(y−z),[0,1]×[0,3]×[0,3]

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Chapter 16 Solutions

Evaluate $\underset{B}{∭} f (x, y, z) d v$ for the specified function $f$ and box $B .$

$f (x, y, z) = (x - y) (y - z), [0, 1] \times [0, 3] \times [0, 3]$