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Unformatted text preview: ds to use. There is only one other thing to worry about in terms of the surface area formula. The ds will introduce a new differential to the integral. Before integrating make sure all the variables are in terms of this new differential. For example if we have parametric equations well use the third ds and then we’ll need to make sure and substitute for the x or y depending on which axis we rotate about to get everything in terms of t . Likewise, if we have a function in the form then we’ll use the second ds and if the rotation is about the yaxis we’ll need to substitute for the x in the integral. On the other hand if we rotate about the xaxis we won’t need to do a substitution for the y . Keep these rules in mind and you’ll always be able to determine which formula to use and how to correctly do the integral....
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This note was uploaded on 11/10/2011 for the course MATH 136 taught by Professor Prellis during the Fall '08 term at Rutgers.
 Fall '08
 prellis
 Arc Length

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