Explanation Given: The region E is the tetrahedron with vertices ( 0 , 0 , 0 ) , ( 0 , 0 , 1 ) , ( 0 , 2 , 0 ) , ( 2 , 2 , 0 ) . Formula used: The volume of the given solid is given by, V = ∭ E d V . Calculation: From the given conditions, it is observed that the equations of the planes which is the sides of the tetrahedron are y = 2 , x = y and y + 2 z = 2 . Then, the volume of the given solid is, V = ∭ E d V = ∫ 0 2 ∫ 0 y ∫ 0 2 − y 2 d z d x d y Integrate with respect to z and apply the limit. V = ∫ 0 2 ∫ 0 y [ z ] 0 2 − y 2 d x d y = ∫ 0 2 ∫ 0 y [ 2 − y 2 − 0 ] d x d y = ∫ 0 2 ∫ 0 y ( 1 − y 2 ) d x d y Integrate with respect to y and apply the limit

8th Edition

ISBN: 9781285741550

Author: James Stewart

Publisher: Cengage Learning

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Chapter 15, Problem 37RE

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To find: The volume of the given solid.

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Chapter 15, Problem 36RE

Chapter 15, Problem 38RE

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Chapter 15 Solutions

Calculus: Early Transcendentals

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The volume of the given solid.

Solution Summary: The author explains that the volume of the given solid is 23.

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