Explanation Explanation Given 1. Function f ( x , y , z ) = z . 13. Region of integration in the threedimensional space is given by 0 ≤ z ≤ x 2 + y 2 ≤ 9 Formula 1. Equations to transform Cartesian coordinates into cylindrical polar coordinates 2. 0 ≤ θ ≤ 2 π where r ≥ 0 and . x = r cos ( θ ) , y = r sin ( θ ) , and z 2. Volume element in cylindrical polar coordinates rdrdzd θ . Calculation The given volume, V , is 0 ≤ z ≤ x 2 + y 2 ≤ 9 . This can be described using cylindrical polar coordinates as x = r cos ( θ ) , x = r cos ( θ ) , and z where z ≤ x 2 + y 2 ≤ 9 ( z ≤ r ≤ 3 ) , 0 ≤ z ≤ 9 and 0 ≤ θ ≤ 2 π . Then the required volume integral can be computed as follows...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.4, Problem 32E

To determine

To find

Volume integral of the function $f (x, y, z) = z$ over the region $0 \leq z \leq x^{2} + y^{2} \leq 9$

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Chapter 16.4, Problem 31E

Chapter 16.4, Problem 33E

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Chapter 16 Solutions

CALCULUS (CLOTH)

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To find Volume integral of the function f ( x , y , z ) = z over the region 0 ≤ z ≤ x 2 + y 2 ≤ 9

Solution Summary: The author explains the volume integral of the function f (x, y ) = z over the region of integration in the threedimensional space.

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To find

Volume integral of the function $f (x, y, z) = z$ over the region $0 \leq z \leq x^{2} + y^{2} \leq 9$

Want to see the full answer?

Chapter 16 Solutions

To find Volume integral of the function f ( x , y , z ) = z over the region 0 ≤ z ≤ x 2 + y 2 ≤ 9

Solution Summary: The author explains the volume integral of the function f (x, y ) = z over the region of integration in the threedimensional space.

Videos

To find Volume integral of the function f(x,y,z)=zover the region 0≤z≤x2+y2≤9

Want to see the full answer?

Chapter 16 Solutions

To find

Volume integral of the function $f (x, y, z) = z$ over the region $0 \leq z \leq x^{2} + y^{2} \leq 9$