Explanation Given info. f ( x , y , z ) = x ( y + z ) 2 [ 0 , 2 ] × [ 2 , 4 ] × [ − 1 , 1 ] Concept used: Theorem for triple integrals. If f is continuous on the rectangular box B = [ a × b ] × [ c , d ] × [ r , x ] ∭ B 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 ( Given expression ) [ 0 , 2 ] × [ 2 , 4 ] × [ − 1 , 1 ] ( given box ) Putting the value of function and limits = ∫ − 1 1 ∫ 2 4 ∫ 0 2 x ( y + z ) 2 d x d y d z Integrate w.r.t x keeping y and z as constant = ∫ − 1 1 ∫ 2 4 [ ∫ 0 2 x ( y + z ) 2 d x ] d y d z ( r e w r i t e the expression ) = ∫ − 1 1 ∫ 2 4 [ x 2 2 ( y + z ) 2 ] 0 2 d y d z ( p u t t i n g the value of limit x ) = ∫ − 1 1 ∫ 2 4 4 2 ( y + z ) 2 d y d z ( after putting the limit of x ) = 2 ∫ − 1 1 ∫ 2 4 1 ( y + z ) d y d z ( taking constant outside ) Integrate w...

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.3, Problem 4E

To determine

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

$f (x, y, z) = \frac{x}{{(y + z)}^{2}}, [0, 2] \times [2, 4] \times [- 1, 1]$

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Chapter 16.3, Problem 3E

Chapter 16.3, Problem 5E

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Chapter 16 Solutions

CALCULUS (CLOTH)

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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 + z ) 2 , [ 0 , 2 ] × [ 2 , 4 ] × [ − 1 , 1 ]

Solution Summary: The author explains how to determine the value of function and limits in a given box.

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

$f (x, y, z) = \frac{x}{{(y + z)}^{2}}, [0, 2] \times [2, 4] \times [- 1, 1]$

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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 + z ) 2 , [ 0 , 2 ] × [ 2 , 4 ] × [ − 1 , 1 ]

Solution Summary: The author explains how to determine the value of function and limits in a given box.

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Evaluate ∭Bf(x,y,z)dvfor the specified function f and box B. f(x,y,z)=x(y+z)2,[0,2]×[2,4]×[−1,1]

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Chapter 16 Solutions

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

$f (x, y, z) = \frac{x}{{(y + z)}^{2}}, [0, 2] \times [2, 4] \times [- 1, 1]$