Explanation Given info: f ( x , y , z ) = ( x + y − z ) 2 b o x B . [ 0 , a ] × [ 0 , b ] × [ 0 , c ] Concept used: If f is continuous on the rectangular b o x B = [ a × b ] × [ c , d ] × [ r , s ] then ∭ R f ( x , y , z ) d v = ∫ r s ∫ c d ∫ a b f ( x , y , z ) d x d y d z Calculation: ∭ B f ( x , y , z ) d v f ( x , y , z ) = ( x + y + z ) 2 b o x B : [ 0 , a ] × [ 0 , b ] × [ 0 , c ] Putting these value in above integration ∫ 0 c ∫ 0 b ∫ 0 a ( x + y − z ) 2 d x d y d z Use ( a + b − c ) 2 = a 2 + b 2 + c 2 + 2 a b − 2 b c − 2 c a ∫ 0 c ∫ 0 b ∫ 0 a ( x 2 + y 2 + z 2 + 2 x y − 2 y z − 2 z x ) d x d y d z Integrate w . r . t x keeping y and z as constant = ∫ 0 c ∫ 0 b [ ∫ 0 a ( x 2 + y 2 + z 2 + 2 x y − 2 y z − 2 z x ) d x ] d y d z = ∫ 0 c ∫ 0 b [ x 3 3 + x y 2 + x z 2 + x 2 y − 2 x y z − z x 2 ] 0 a d y d z ( integrate w .r .t to x ) ( p u t t i n g the limit of x ) = ∫ 0 c ∫ 0 b ( a 3 3 + a y 2 + a z 2 + a 2 y − 2 a y z − a 2 z ) d y d z Integrate w ...

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ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.3, Problem 8E

To determine

Evaluate $\underset{B}{∭} f (x, y, z) d v$ for the specified function & $b o x B$ given below.

$f (x, y, z) = {(x + y - z)}^{2}, [0, a] \times [0, b] \times [0, c]$

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Chapter 16.3, Problem 7E

Chapter 16.3, Problem 9E

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Chapter 16 Solutions

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Evaluate ∭ B f ( x , y , z ) d v for the specified function & b o x B given below. f ( x , y , z ) = ( x + y − z ) 2 , [ 0 , a ] × [ 0 , b ] × [ 0 , c ]

Solution Summary: The author explains how to determine if f is continuous on the rectangular b o x B.

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Evaluate $\underset{B}{∭} f (x, y, z) d v$ for the specified function & $b o x B$ given below.

$f (x, y, z) = {(x + y - z)}^{2}, [0, a] \times [0, b] \times [0, c]$

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Chapter 16 Solutions

Evaluate ∭ B f ( x , y , z ) d v for the specified function &amp; b o x B given below. f ( x , y , z ) = ( x + y − z ) 2 , [ 0 , a ] × [ 0 , b ] × [ 0 , c ]

Solution Summary: The author explains how to determine if f is continuous on the rectangular b o x B.

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Evaluate ∭Bf(x,y,z)dv for the specified function &boxBgiven below. f(x,y,z)=(x+y−z)2,[0,a]×[0,b]×[0,c]

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Chapter 16 Solutions

Evaluate ∭ B f ( x , y , z ) d v for the specified function & b o x B given below. f ( x , y , z ) = ( x + y − z ) 2 , [ 0 , a ] × [ 0 , b ] × [ 0 , c ]

Evaluate $\underset{B}{∭} f (x, y, z) d v$ for the specified function & $b o x B$ given below.

$f (x, y, z) = {(x + y - z)}^{2}, [0, a] \times [0, b] \times [0, c]$