Explanation Given: f ( x , y , z ) = x y + z 2 and B : [ − 2 , 2 ] × [ 0 , 1 ] × [ 0 , 2 ] Formula used: The integral formula ∫ x n d x = x n + 1 n + 1 Calculation: The triple integral of f ( x , y , z ) over for B is equals to the iterated integral: ∫ ∫ ∫ B f ( x , y , z ) d V = ∫ − 2 2 ∫ 0 1 ∫ 0 2 ( x y + z 2 ) d z d y d x First, integrating the inner integral treating x and y as constant ∫ − 2 2 ∫ 0 1 [ x y z + z 3 3 ] 0 2 d y d x = ∫ − 2 2 ∫ 0 1 ( 2 x y + 8 3 ) d y d x Now integrate middle integral, treating x as c

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ISBN: 9781319309671

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 15.3, Problem 2E

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Evaluate ∫∫∫Bf(x,y,z)dV where f(x,y,z)=xy+z2 and B:[−2,2]×[0,1]×[0,2]

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Chapter 15.3, Problem 1E

Chapter 15.3, Problem 3E

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Chapter 15 Solutions

CALCULUS: EARLY TRANS 4TH ED W/ ACCESS

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Evaluate ∫ ∫ ∫ B f ( x , y , z ) d V where f ( x , y , z ) = x y + z 2 and B : [ − 2 , 2 ] × [ 0 , 1 ] × [ 0 , 2 ]

Solution Summary: The author analyzes how the triple integral of f(x,y,z) over for B is equal to the iterated integral.

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Evaluate ∫∫∫Bf(x,y,z)dV where f(x,y,z)=xy+z2 and B:[−2,2]×[0,1]×[0,2]

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Chapter 15 Solutions