Explanation Given: The equation of volume of solid x 2 + z 2 = 1 , y 2 + z 2 = 1 , first octant. Formula used: The volume of a solid is provided by, V = ∬ R f ( x , y ) d A Where, f ( x , y ) = z Calculation: Consider the solid bounded by the graphs of the equations. x 2 + z 2 = 1 , y 2 + z 2 = 1 , first octant The objective is to set up the double integral to find the volume of the solid. The intersection of these two graphs is: From the given two equations, 1 − x 2 = 1 − y 2 − x 2 = − y 2 x = y (Since graph is in 1 st octant) The limits of the x and y are: R = { ( x , y ) 0 ≤ x ≤ 1 , 0 ≤ y ≤ x } The graph of the region is, Here, from the graph there are two equal regions. One is above the line x = y and the other is Below the line x = y . The volume of the solid bounded y the region R is given by, V = ∬ R f ( x , y ) d A Let, z = f ( x , y ) = 1 − x 2 Therefore the volume of the solid bounded by the given curves in first octant is given by, V = ∬ R f ( x , y ) d A = ∬ R 1 f ( x , y ) d A + ∬ R 2 f (

Calculus: Early Transcendental Functions (MindTap Course List)

6th Edition

ISBN: 9781285774770

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 14.2, Problem 29E

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To calculate: The volume of solid bounded by the graphs of the equations x2+z2=1,y2+z2=1, first octant.

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Chapter 14.2, Problem 30E

Chapter 14.2, Problem 33E

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SET-UP, Do Not Evaluate a triple integral to find the volume of the solid in the first octant that is bounded by the plane x +2y + 3z = 6 and the cylinder, x' + y = 4.

Chapter 14 Solutions

Calculus: Early Transcendental Functions (MindTap Course List)

Ch. 14.1 - Evaluate the iterated integral: 0433cosrdrd Ch. 14.1 - Prob. 1E Ch. 14.1 - Evaluate the integral: xx2yxdy Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Evaluate the integral: 04x2x2ydy Ch. 14.1 - Evaluate the integral: x3x(x2+3y2)dy Ch. 14.1 - Evaluate the integral: eyyylnxxdx;y0 Ch. 14.1 - Evaluate the integral: 1y21y2(x2+y2)dx Ch. 14.1 - Evaluate the integral: 0x2yeyxdy

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The volume of solid bounded by the graphs of the equations x 2 + z 2 = 1 , y 2 + z 2 = 1 , first octant.

Solution Summary: The author explains how to calculate the volume of a solid bounded by the graphs of the equations.

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To calculate: The volume of solid bounded by the graphs of the equations x2+z2=1,y2+z2=1, first octant.

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Chapter 14 Solutions