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Unformatted text preview: the ds that we used. In this case however, we will always have to substitute for the variable. The ds that we use for parametric equations introduces a dt into the integral and that means that everything needs to be in terms of t . Therefore, we will need to substitute the appropriate parametric equation for x or y depending on the axis of rotation. Let’s take a quick look at an example. Example 1 Determine the surface area of the solid obtained by rotating the following parametric curve about the xaxis. Solution We’ll first need the derivatives of the parametric equations. Before plugging into the surface area formula let’s get the ds out of the way. Notice that we could drop the absolute value bars since both sine and cosine are positive in this range of θ given. Now let’s get the surface area and don’t forget to also plug in for the y ....
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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
 Calculus, Equations, Parametric Equations

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