5.6.notes - MAC 2233/001-006 Business Calculus Spring 2011 CRN 1257712582 Assistants V Kumari Y Xi D Ozcan M Assad T Zerihun A Rai On the Midpoint

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MAC 2233/001-006 Business Calculus, Spring 2011 CRN: 12577–12582 Assistants : V. Kumari, Y. Xi, D. Ozcan, M. Assad, T. Zerihun, A. Rai On the Midpoint Rule for numerically estimating the value of a deFnite integral Assume that f is continuous and nonnegative on the interval [ a, b ]. The defnite integral is equal to the area oF the region “under” the graph oF y = f ( x ) From x = a to x = b . We saw in a previous example that iF an antiderivative oF f can be Found, then the exact value oF the area (and oF the defnite integral) can be obtained. However, not all Functions f have easy antiderivatives. In such cases, we would use numerical integration. There are many sophisticated methods For numerical integration. We shall consider a very elementary method, called the Midpoint Rule, to estimate the value oF the area oF the region bounded by y = f ( x ), x = a , x = b and y = 0. So we would want to estimate the area oF shaded region in the diagram below. b
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This note was uploaded on 01/02/2012 for the course MAC 2233 taught by Professor Danielyan during the Fall '08 term at University of South Florida - Tampa.

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5.6.notes - MAC 2233/001-006 Business Calculus Spring 2011 CRN 1257712582 Assistants V Kumari Y Xi D Ozcan M Assad T Zerihun A Rai On the Midpoint

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