Explanation Given info: The region bounded by z = 1 − y 2 , y = x 2 and the plane z = 0 and order of integration d z d y d x Concept used: Draw the diagram identify the bounded region find out the limit of x . Take projection of bounded region in z y plane after that decide that limit of y and x . Calculation: Draw the diagram with the help of z = 1 − y 2 , y = x 2 , z = 0 x − Is only function of y for bounded region solving the inequality for x x 2 ≤ y | x | ≤ y − y ≤ x ≤ y Take the projection of bounded region on z y plane. From the above diagram it becomes clear that 0 ≤ z ≤ 1 − y 2 0 ≤ y ≤ 1 ∭ w d v = ∭ w d x d z d y w : 0 ≤ y ≤ 1 , 0 ≤ z ≤ 1 − y 2 , − y ≤ x ≤ y . ( Putting the limit of in sume order ) = ∫ 0 1 ∫ 0 1 − y 2 ∫ − y 1 y d x d z d y Integrate with respect to x = ∫ 0 1 ∫ To determine ( b ) Calculate the volume of the region w bounded by z = 1 − y 2 , y = x 2 and the plane z = 0 as triple integration of following orders. ( b ) d y d z d x

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 16.3, Problem 32E

To determine

$(a)$

Calculate the volume of the region $w$ bounded by $z = 1 - y^{2}, y = x^{2}$ and the plane $z = 0$ as triple integration of following orders. $(a) d x d z d y$

To determine

$(b)$

Calculate the volume of the region $w$ bounded by $z = 1 - y^{2}, y = x^{2}$ and the plane $z = 0$ as triple integration of following orders. $(b) d y d z d x$

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Chapter 16.3, Problem 31E

Chapter 16.3, Problem 33E

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( a ) Calculate the volume of the region w bounded by z = 1 − y 2 , y = x 2 and the plane z = 0 as triple integration of following orders. ( a ) d x d z d y

Solution Summary: The author explains how to determine the volume of the region w bounded by z = 1 y 2 and x 2 as triple integration of following orders.

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$(a)$

Calculate the volume of the region $w$ bounded by $z = 1 - y^{2}, y = x^{2}$ and the plane $z = 0$ as triple integration of following orders. $(a) d x d z d y$

$(b)$

Calculate the volume of the region $w$ bounded by $z = 1 - y^{2}, y = x^{2}$ and the plane $z = 0$ as triple integration of following orders. $(b) d y d z d x$

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Chapter 16 Solutions

( a ) Calculate the volume of the region w bounded by z = 1 − y 2 , y = x 2 and the plane z = 0 as triple integration of following orders. ( a ) d x d z d y

Solution Summary: The author explains how to determine the volume of the region w bounded by z = 1 y 2 and x 2 as triple integration of following orders.

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(a) Calculate the volume of the region w bounded by z=1−y2,y=x2 and the plane z=0 as triple integration of following orders.(a)dxdzdy

(b) Calculate the volume of the region w bounded by z=1−y2,y=x2 and the plane z=0 as triple integration of following orders.(b)dydzdx

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Chapter 16 Solutions

$(a)$

Calculate the volume of the region $w$ bounded by $z = 1 - y^{2}, y = x^{2}$ and the plane $z = 0$ as triple integration of following orders. $(a) d x d z d y$

$(b)$

Calculate the volume of the region $w$ bounded by $z = 1 - y^{2}, y = x^{2}$ and the plane $z = 0$ as triple integration of following orders. $(b) d y d z d x$