Find the surface area of revolution generated by the following curve (given in parametric form):
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I managed to get the following:
Surface Area =
How on Earth do I integrate this? Thanks for any help
I would first start of by rewriting the integrand. Recall that
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I will take the positive square root since surface area must be positive. Therefore, the integrand can be simplified to:
Thus the integral becomes:
Apply a substitution...primarily . Thus . Solving for , we get .
Before we substitute, we can change the limits of integration as well. The upper limit will become and the lower limit will become .
Now, the integral can be rewritten as:
evaluating the integral we get:
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Hope that helped you out!