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## AnalyticGeometryandCalculusABIOLOGICALEXAMPLES

by: Mustafa Wilderman

20

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# AnalyticGeometryandCalculusABIOLOGICALEXAMPLES MATH241

Marketplace > University of Delaware > Mathematics (M) > MATH241 > AnalyticGeometryandCalculusABIOLOGICALEXAMPLES
Mustafa Wilderman
UD
GPA 3.58

Staff

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## Popular in Mathematics (M)

This 2 page Class Notes was uploaded by Mustafa Wilderman on Saturday September 19, 2015. The Class Notes belongs to MATH241 at University of Delaware taught by Staff in Fall. Since its upload, it has received 20 views. For similar materials see /class/207115/math241-university-of-delaware in Mathematics (M) at University of Delaware.

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Date Created: 09/19/15
MATH 241 Section 53 Page 1 The Fundamental Theorem of Calculus Part 1 If fis continuous on a b then the function 9 defined by gX Jft dz for a s X s b is continuous on a b and differentiable on a b and g X fX The Fundamental Theorem of Calculus Part 2 If fis continuous on a b then jfxdx FbFa a where F is any antiderivative of feg F f MATH 241 Section 53 Page 2 FTC Part1 means If a function is integrated and the result is differentiated we arrive back at the original function FTC Part 2 means If we take a function then differentiate it and then integrate the result we arrive back at the original function but in the form of the difference of the function evaluated at the 2 endpoints Taken together the two parts ofthe FTC say that differentiation and integration are inverse processes Each undoes what the other does This is the most important theorem of calculus and in fact one of the greatest accomplishments of the human mind

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