Explanation Given: The function is z = 2 1 + x 2 + y 2 and the limits are z = 0 , y = 0 , x = 0 , y = − 0.5 x + 1 . Formula used: V = ∬ R f ( x , y ) d A Calculation: From the given equations: z = 2 1 + x 2 + y 2 …… (1) z = 0 …… (2) y = 0 …… (3) x = 0 …… (4) y = − 0.5 x + 1 …… (5) Substitute equation (3) and (4) in the equation (1), to get, z = 2 1 + 0 2 + 0 2 = 2 Therefore, z limits and y limits are 0 and 2, and 0 and − 0.5 x + 1 , respectively. If f can be integrated over a plane region R where f ( x , y ) ≥ 0 for all ( x , y ) in R , then the volume of the solid region that lies above R and below the graph of f is: V = ∬ R f ( x , y ) d A The solid region is shown below:

11th Edition

ISBN: 9781337275378

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 14.2, Problem 43E

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To calculate: What the volume of the solid z=21+x2+y2, bounded by the graphs of the equations z=0,y=0,x=0,y=−0.5x+1, will be when computed with the help of computer algebra system.

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What the volume of the solid z = 2 1 + x 2 + y 2 , bounded by the graphs of the equations z = 0 , y = 0 , x = 0 , y = − 0.5 x + 1 , will be when computed with the help of computer algebra system.

Solution Summary: The author explains how to calculate the volume of the solid z=21+x2.

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To calculate: What the volume of the solid z=21+x2+y2, bounded by the graphs of the equations z=0,y=0,x=0,y=−0.5x+1, will be when computed with the help of computer algebra system.

Chapter 14 Solutions