[PDF] Second Fundamental Theorem of Calculus



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MATH 222 Second Semester Calculus

Math 222 – 2nd Semester Calculus Lecture notes version 1 1 (Fall 2015) „is is a self contained set of lecture notes for Math 222 „e notes were wri−en by Sigurd Angenent, as part ot the MIU calculus project Some problems were contributed by A Miller „eLATEX•les, aswellastheInkscapeandOctave•leswhichwereusedtoproduce



Second Fundamental Theorem of Calculus

Second Fundamental Theorem of Calculus Let f be a continuous function de ned on an interval I Fix a point a in I and de ne a function F on I by F(x) = Z x a f(t)dt: Then F is an antiderivative of f on the interval I, i e F0(x) = f(x) on I A proof of the Second Fundamental Theorem of Calculus is given on pages 318{319 of the textbook We



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of by a constant fails to produce a second linearly independent solution, suppose we try multiplying by a functioninstead The simplest such function would be , so let’s see if is also a solution Substituting into the differential equation gives The first term is zero because ; the second term is zero because solves the auxiliary equation



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Oct 09, 2012 · CALCULUS MADE EASY 6 took dxto mean numerically, say, 1 60 of x, then the second term would be 2 60 of x, whereas the third term would be 1 3600 of x2 This last term is clearly less important than the second But if we go further and take dxto mean only 1 1000 of x, then the second term will be 2 1000 of x2, while the third term will be only 1



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BASIC CALCULUS REFRESHER Ismor Fischer, Ph D Dept of Statistics UW-Madison 1 Introduction This is a very condensed and simplified version of basic calculus, which is a prerequisite for many courses in Mathematics, Statistics, Engineering, Pharmacy, etc It is not comprehensive, and



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Seconde/Ensembledenombresetcalculs 1 Calcul dans N, Z et Q: Exercice 8270 Définitions: On classe les nombres suivants leurs natures: Tous les nombres admettant une écriture décimale for-

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