When to use the Shell Method or Washer Method to Calculate VolumeDate: 2/26/96 at 20:10:5 From: Anonymous Subject: calculus help I'm taking AB Calculus and we are learning about applications of definite integrals. We recently learned about the washer method and shell method. However, I was wondering which method to use in different situations. Thanks a lot. T.J. Pascalides@aol.com Date: 2/27/96 at 13:24:24 From: Doctor Ken Subject: Re: calculus help Hello! Well, to tell the truth, it just depends on whichever method is easiest.Sometimes you'll be able to do both with about the same ease, for example find the volume of the object formed when the triangle with vertices (0,0), (1,0), and (1,1) is revolved around the y-axis. Sometimes it just doesn't make sense to do it one way or the other, though. For instance, find the volume of the object formed when a piece (from 0 to 5Pi, for instance) of the Sine curve is revolved around the x-axis. It would be pretty silly to use the shell method, because then you'd have to try to take horizontal area slices between the Sine curve and the x-axis. So the washer method is pretty much the way to go on this one. But in general, you just kind of have to look at the problem and decide whether horizontal slices or vertical slices are easier to work with for your function. -Doctor Ken, The Math Forum |
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