Explanation Theorem used: Volume under a surface: If f ( x , y ) ≥ 0 over a rectangle R = { ( x , y ) | a ≤ x ≤ b , c ≤ y ≤ d } , then the volume of the solid formed by graphing f over the rectangle R is given by V = ∬ R f ( x , y ) d A . Calculation: Use the online graphing calculator to sketch the graph of y = 1 − x 2 , y = 0 for 0 ≤ x ≤ 1 as shown in below Figure 1. From Figure 1, it is observed that the region can be defined as R = { ( x , y ) | 0 ≤ y ≤ 1 − x 2 , 0 ≤ x ≤ 1 } . Now obtain the volume of the solid f ( x , y ) = 4 . First, compute the integral with respect to y . ∫ 0 1 ∫ 0 1 − x 2 4 d y d x = ∫ 0 1 [ 4 ∫ 0 1 − x 2 d y ] d x = ∫ 0 1 4 [ y ] 0 1 − x 2 d x Apply the limit value for y

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14th Edition

ISBN: 9780137553341

Author: Raymond Barnett, Michael Ziegler

Publisher: PEARSON+

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Chapter 14.7, Problem 41E

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To find: The volume of the solid under the graph of f(x,y)=4 and to sketch the region R.

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Chapter 14.7, Problem 40E

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Chapter 14 Solutions

Pearson eText for College Mathematics for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

Ch. 14.1 - Matched Problem 1 Find C(20, 10) for the cost...Ch. 14.1 - Prob. 2MP Ch. 14.1 - Prob. 3MP Ch. 14.1 - Prob. 4MP Ch. 14.1 - Prob. 5MP Ch. 14.1 - Prob. 6MP Ch. 14.1 - Prob. 7MP Ch. 14.1 - Prob. 1ED Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E

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The volume of the solid under the graph of f ( x , y ) = 4 and to sketch the region R .

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