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Unformatted text preview: slices until we reach the height of the cylinder. Any case will involve adding up the slices to find a quantity; in this case it is volume, but it could easily also be mass. So to add up all these slices, we find the volume of each individual slice and add them together. But because we want these slices to be infinitely thin, we will take the limit of these slices as the thickness goes to zero. This limitsum directly translates into an integral. The limit as the thickness goes to zero of the sum of all of our slices means exactly the same thing as the integral of the volume of each slice from 0 to the height. By definition, the integral is the sum of a bunch of infinitely small pieces. Then of course, solving the integral, gives the total valuein this case, the volume of the cylinder....
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This note was uploaded on 04/02/2008 for the course MATH 116 taught by Professor Irena during the Winter '07 term at University of Michigan.
 Winter '07
 Irena
 Calculus, Equations

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