Chap6_Sec3 - 6 APPLICATIONS OF INTEGRATION APPLICATIONS...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
APPLICATIONS OF INTEGRATION APPLICATIONS OF INTEGRATION 6
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
6.3 Volumes by Cylindrical Shells APPLICATIONS OF INTEGRATION In this section, we will learn: How to apply the method of cylindrical shells to find out the volume of a solid.
Background image of page 2
Some volume problems are very difficult to handle by the methods discussed in Section 6.2 VOLUMES BY CYLINDRICAL SHELLS
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Let’s consider the problem of finding the volume of the solid obtained by rotating about the y -axis the region bounded by y = 2 x 2 - x 3 and y = 0. VOLUMES BY CYLINDRICAL SHELLS
Background image of page 4
If we slice perpendicular to the y -axis, we get a washer. However, to compute the inner radius and the outer radius of the washer, we would have to solve the cubic equation y = 2 x 2 - x 3 for x in terms of y . That’s not easy. VOLUMES BY CYLINDRICAL SHELLS
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Fortunately, there is a method—the method of cylindrical shells—that is easier to use in such a case. VOLUMES BY CYLINDRICAL SHELLS
Background image of page 6
The figure shows a cylindrical shell with inner radius r 1 , outer radius r 2 , and height h . CYLINDRICAL SHELLS METHOD
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Its volume V is calculated by subtracting the volume V 1 of the inner cylinder from the volume of the outer cylinder V 2 . CYLINDRICAL SHELLS METHOD
Background image of page 8
Thus, we have: 2 1 2 2 2 1 2 2 2 1 2 1 2 1 2 1 2 1 ( ) ( )( ) 2 ( ) 2 V V V r h r h r r h r r r r h r r h r r π = - = - = - = + - + = - CYLINDRICAL SHELLS METHOD
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
r = r 2 r 1 (thickness of the shell) and (average radius of the shell). Then, this formula for the volume of a
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/06/2012 for the course MATH 2414.S01 taught by Professor Alans.grave during the Fall '11 term at Collins.

Page1 / 37

Chap6_Sec3 - 6 APPLICATIONS OF INTEGRATION APPLICATIONS...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online