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Unformatted text preview: MAT 271 Maple Project: Approximating π The goal of this project is to approximate the number π to thirty decimal places using two methods: approximate integration and approximation by series. You will do this in several steps. The numbered steps are “problems” for you to do, and the paragraphs in between will help provide the overall picture. You will first approximate π by approximating an integral whose exact value is π . For reasons which should become clear, you will only approximate π to 6 places. (1) Pick an integral, using the chart below. If your first name begins with: then your integral is: A–F, √ 2 / 4 Z 8 √ 1 4 x 2 dx G–K, 1 Z 20 x 4 x 10 + 1 dx L–Z, √ 2 Z 4 √ 2 24 x √ x 4 1 dx (2) Show that your integral equals π . You may need to use a substitution, such as t = 2 x , t = x 5 , or t = x 2 . (3) Use the Trapezoidal Rule for approximating your integral: Find a value K such that  f 00 ( x )  ≤ K , for all x between the limits of your integral, and where f ( x ) is your integrand (the function being integrated). [You will most likely need Maple for this step.] Once you findstep....
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 Spring '08
 Hurlbert
 Calculus, Approximation, Indian mathematics

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