Explanation Given information: ∫ − 1 1 ∫ 0 y = 1 − x 2 ∫ z = 0 x 2 + y 2 f ( x , y , z ) d z d y d x Formula used: For a continuous function on the region θ 1 ≤ θ ≤ θ 2 , r 1 ( θ ) ≤ r ≤ r 2 ( θ ) , z 1 ( r , θ ) ≤ z ≤ z 2 ( r , θ ) , the triple integral ∭ W f ( x , y , z ) d V = ∫ θ 1 θ 2 ∫ r 1 ( θ ) r 2 ( θ ) ∫ z 1 ( r , θ ) z 2 ( r , θ ) f ( r cos θ , r sin θ , z ) r d z d r d θ Calculation: First, express the region in cylindrical coordinates, As region is: W = { ( x , y , z ) : − 1 ≤ x ≤ 1 , 0 ≤ y ≤ 1 − x 2 , 0 ≤ z ≤ x 2 + y 2 } The condition 0 ≤ z ≤ x 2 + y 2 tells that solid is in between xy -plane and the plane z = x 2 + y 2 which lies above the region D = { ( x , y ) : − 1 ≤ x ≤ 2 , 0 ≤ y ≤ 1 − x 2 } Putting x = r cos θ , y = r sin θ in condition y = 1 − x 2

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ISBN: 9781319055905

Author: FRANZOSA

Publisher: VST

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Chapter 15.4, Problem 35E

To determine

Express the triple integral in cylindrical coordinates

∫−11∫0y=1−x2∫z=0x2+y2f(x,y,z)dzdydx

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Chapter 15.4, Problem 34E

Chapter 15.4, Problem 36E

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Chapter 15 Solutions

EBK CALCULUS: EARLY TRANSCENDENTALS

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Express the triple integral in cylindrical coordinates ∫ − 1 1 ∫ 0 y = 1 − x 2 ∫ z = 0 x 2 + y 2 f ( x , y , z ) d z d y d x

Solution Summary: The author explains how to express the triple integral in cylindrical coordinates.

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Express the triple integral in cylindrical coordinates

∫−11∫0y=1−x2∫z=0x2+y2f(x,y,z)dzdydx

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Chapter 15 Solutions

Express the triple integral in cylindrical coordinates ∫ − 1 1 ∫ 0 y = 1 − x 2 ∫ z = 0 x 2 + y 2 f ( x , y , z ) d z d y d x

Solution Summary: The author explains how to express the triple integral in cylindrical coordinates.

Videos

Express the triple integral in cylindrical coordinates ∫−11∫0y=1−x2∫z=0x2+y2f(x,y,z)dzdydx

Want to see the full answer?

Chapter 15 Solutions

Express the triple integral in cylindrical coordinates

∫−11∫0y=1−x2∫z=0x2+y2f(x,y,z)dzdydx