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The region enclosed by the curves y =x and y = 1 is shown below: Cross section area of the solid perpendicular to y-axis = A(y) A(y) = (2x) = 4x = 4y Now, vohume of the required solid is V = [ A(y)dy = 4 ycy

The region enclosed by the curves y =x and y = 1 is shown below: Cross section area of the solid perpendicular to y-axis = A(y) A(y) = (2x) = 4x = 4y Now, vohume of the required solid is V = [ A(y)dy = 4 ycy

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...
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In the attached photo, you can see the solution for the volume between the y=x^2 and y = 1. My question is, why is A(y) = (2x)^2 ? I do not understand where the 2x comes from, my belief was that A(y) = x^2 and I just went from there, I am confused as to where the 2x came from. 

The region enclosed by the curves y =x and y = 1 is shown below: Cross section area of the solid perpendicular to y-axis = A(y) A(y) = (2x) = 4x = 4y Now, vohume of the required solid is V = [ A(y)dy = 4 ycy
Transcribed Image Text:The region enclosed by the curves y =x and y = 1 is shown below: Cross section area of the solid perpendicular to y-axis = A(y) A(y) = (2x) = 4x = 4y Now, vohume of the required solid is V = [ A(y)dy = 4 ycy
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