Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. y = 100 - x2 y = 0 Step 1 Because the axis of revolution is vertical, use a vertical vertical representative rectangle as shown in the figure. 100 80- 20 -10 -5 10 The width Ax indicates that x is the variable of integration. The distance from the center of the rectangle to the axis of revolution is p(x) = x, and the height of the rectangle is h(x) = 100 - Step 2 To find the volume of a solid of revolution with the shell method, use the following formula. Volume = V = 2n P(x)h(x) dx Because x ranges from 0 to 10, the volume of the solid is V = 2m P(x)h(x) dx = 2n (100 - x) dx.

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. y = 100 - x2 y = 0 Step 1 Because the axis of revolution is vertical, use a vertical vertical representative rectangle as shown in the figure. 100 80- 20 -10 -5 10 The width Ax indicates that x is the variable of integration. The distance from the center of the rectangle to the axis of revolution is p(x) = x, and the height of the rectangle is h(x) = 100 - Step 2 To find the volume of a solid of revolution with the shell method, use the following formula. Volume = V = 2n P(x)h(x) dx Because x ranges from 0 to 10, the volume of the solid is V = 2m P(x)h(x) dx = 2n (100 - x) dx.

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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