Explanation Given info: f ( x , y , x ) = x e y − 2 z 0 ≤ x ≤ 2 , 0 ≤ y ≤ 1 , 0 ≤ z ≤ 1 Concept used: Limit of x , y , z are constant so integration can be performed in any order, but should be Careabout limit on integration sign should be also in same order. Calculation: ∭ B f ( x , y , z ) d v f ( x , y , z ) = x e y − 2 z 0 ≤ x ≤ 2 0 ≤ y , ≤ 1 0 ≤ z ≤ 1 Putting value of limit and function = ∫ 0 2 ∫ 0 1 ∫ 0 1 x e y − 2 z . d z d y d z ( use e y − 2 z = e y . e y − 2 z ∫ e 0 x d x = e x a ) = ∫ 0 2 ∫ 0 1 ∫ 0 1 x e y . e − 2 z d z d y d x First perform integration with respect to z , as x and y as constant = ∫ 0 2 ∫ 0 1 [ ∫ 0 1 x e y e − 2 z d z ] d y d x ( write into appropriate form ) ( integrate with respect to z keeping y and x as constant ) = ∫ 0 2 ∫ 0 1 [ x e y e − 2 z − 2 ] 0 1 d y d x Putting the value of limit of z = ∫ 0 2 ∫ 0 1 x e y ( e − 2 ( 1 ) − e − 2 × 0 ) d y d x − 2 ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 16.3, Problem 3E

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

$f (x, y, z) = x e^{y - 2 z}, 0 \leq x \leq 2, 0 \leq y \leq 1, 0 \leq z \leq 1$

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Chapter 16.3, Problem 2E

Chapter 16.3, Problem 4E

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Chapter 16 Solutions

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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 e y − 2 z , 0 ≤ x ≤ 2 , 0 ≤ y ≤ 1 , 0 ≤ z ≤ 1

Solution Summary: The author evaluates the function f and box B, and explains how to calculate the value of limit and function.

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

$f (x, y, z) = x e^{y - 2 z}, 0 \leq x \leq 2, 0 \leq y \leq 1, 0 \leq z \leq 1$

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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 e y − 2 z , 0 ≤ x ≤ 2 , 0 ≤ y ≤ 1 , 0 ≤ z ≤ 1

Solution Summary: The author evaluates the function f and box B, and explains how to calculate the value of limit and function.

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Evaluate ∭Bf(x,y,z)dv for the specified function f and box B. f(x,y,z)=xey−2z,0≤x≤2,0≤y≤1,0≤z≤1

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Chapter 16 Solutions

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

$f (x, y, z) = x e^{y - 2 z}, 0 \leq x \leq 2, 0 \leq y \leq 1, 0 \leq z \leq 1$