Cylindrical Shells On a sheet of graph paper, carefully graph the region bounded by x = 0, y = 0, y = 4-2x , rotated about the line x = -1. Scale your graph so that the bounded region takes up a significant portion of the page. Yes, make a new and separate graph. Draw a characteristic rectangle that represents a "slice" of the solid. Label the dimensions of the cylinder generated - radius, height, and thickness. Set up the integral to determine the volume of the solid. Evaluate the integral.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter8: Areas Of Polygons And Circles
Section8.1: Area And Initial Postulates
Problem 55E
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Cylindrical Shells

  • On a sheet of graph paper, carefully graph the region bounded by x = 0, y = 0, y = 4-2x , rotated about the line x = -1. Scale your graph so that the bounded region takes up a significant portion of the page. Yes, make a new and separate graph.
  • Draw a characteristic rectangle that represents a "slice" of the solid.
  • Label the dimensions of the cylinder generated - radius, height, and thickness.
  • Set up the integral to determine the volume of the solid.
  • Evaluate the integral.

 

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