5.4.notes - MAC 2233/001-006 Business Calculus, Spring 2011...

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Unformatted text preview: 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 area and the definite integral We follow the definition in the text. We shall assume always that f is continuous on the closed interval [ a, b ]. Assume for now that f is nonnegative on [ a, b ]. Then the definite integral of f from a to b is written as integraltext b a f ( x )d x and is defined to be integraldisplay b a f ( x )d x = area of the shaded region in the diagram below . b a Note: The shaded region is the region bounded by y = f ( x ), x = a , x = b and y = 0. Observe that as the value of a definite integral is a number (independent of x ), the variable x in integraltext b a f ( x )d x is a “dummy” variable in the sense that the value of the definite integral does not depend on x . Therefore, we can replace all appearances of x by another variable, say t , and the end result is the same. That is, integraldisplay b a f ( x )d x = integraldisplay...
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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.

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5.4.notes - MAC 2233/001-006 Business Calculus, Spring 2011...

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