Explanation Given: f ( x , y ) = 1 − ( x 2 + y 2 ) Calculation: The projection of the surface z = f ( x , y ) = 1 − ( x 2 + y 2 ) onto x − y plane is the unit circle x 2 + y 2 = 1 In polar coordinates it can be represented as D : 0 ≤ θ ≤ 2 π , 0 ≤ r ≤ 1 Thus, the volume of the region between the graph of the function f ( x , y ) = 1 − ( x 2 + y 2 ) and the xy -plane is determined as V = ∫ 0 2 π

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 16, Problem 25CRE

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The volume of the region between the graph of the function $f (x, y) = 1 - (x^{2} + y^{2})$ and the xy-plane.

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Chapter 16, Problem 24CRE

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The volume of the region between the graph of the function f ( x , y ) = 1 − ( x 2 + y 2 ) and the xy -plane.

Solution Summary: The author explains how the volume of the region between the graph and the xy -plane is determined.

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To calculate:

The volume of the region between the graph of the function $f (x, y) = 1 - (x^{2} + y^{2})$ and the xy-plane.

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Chapter 16 Solutions

The volume of the region between the graph of the function f ( x , y ) = 1 − ( x 2 + y 2 ) and the xy -plane.

Solution Summary: The author explains how the volume of the region between the graph and the xy -plane is determined.

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To calculate: The volume of the region between the graph of the function f(x,y)=1−(x2+y2)and the xy-plane.

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Chapter 16 Solutions

To calculate:

The volume of the region between the graph of the function $f (x, y) = 1 - (x^{2} + y^{2})$ and the xy-plane.