Explanation Given information: ∭ W x y z d V , where W = { 0 ≤ x ≤ 1 , x ≤ y ≤ 1 , x ≤ z ≤ x + y } Formula used: The integral formula ∫ x n d x = x n + 1 n + 1 Calculation: To evaluate ∭ W x y z d V , where W = { 0 ≤ x ≤ 1 , x ≤ y ≤ 1 , x ≤ z ≤ x + y } First, convert this integral in integral form as ∭ W x y z d V = ∫ 0 1 ∫ x 1 ∫ x x + y x y z d z d y d x To evaluate this first evaluate the inner integral treating x and y as constant, thus ∫ x x + y x y z d z = x y ∫ x x + y z d z = x y [ z 2 2 ] x x + y = x y 2 [ ( x + y ) 2 − x 2 ] = x y 2 ( y 2 + 2 x y ) = x y 3 2 + x 2 y 2 Now, integrate the above with respec

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ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Chapter 15, Problem 28CRE

To determine

To calculate the triple integral

∭WxyzdV, where W={0≤x≤1,x≤y≤1,x≤z≤x+y}.

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Chapter 15, Problem 27CRE

Chapter 15, Problem 29CRE

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Chapter 15 Solutions

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To calculate the triple integral ∭ W x y z d V , where W = { 0 ≤ x ≤ 1 , x ≤ y ≤ 1 , x ≤ z ≤ x + y } .

Solution Summary: The author explains how to calculate the triple integral displaystyleundersetWiiint

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To calculate the triple integral

∭WxyzdV, where W={0≤x≤1,x≤y≤1,x≤z≤x+y}.

Want to see the full answer?

Chapter 15 Solutions

To calculate the triple integral ∭ W x y z d V , where W = { 0 ≤ x ≤ 1 , x ≤ y ≤ 1 , x ≤ z ≤ x + y } .

Solution Summary: The author explains how to calculate the triple integral displaystyleundersetWiiint

Concept explainers

Videos

To calculate the triple integral ∭WxyzdV, where W={0≤x≤1,x≤y≤1,x≤z≤x+y}.

Want to see the full answer?

Chapter 15 Solutions

To calculate the triple integral

∭WxyzdV, where W={0≤x≤1,x≤y≤1,x≤z≤x+y}.