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 respect to y

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16, 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 16, Problem 27CRE

Chapter 16, Problem 29CRE

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Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

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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 16 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 16 Solutions

To calculate the triple integral

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