Integration anti derivative

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Merced Community College District, Merced College, 2016Merced Community College DistrictIntroduction to IntegrationPart 1: Anti-DifferentiationShairy Balicaoc 2016 Merced CollegeMerced Community College District, Merced College, 201611.1For ReferenceTable of derivativesFunction (f(x))Derivativexnnxn−1exexlnx(n any real number)(x > 0) sinx cosx tanxcotx secx cscxsin−1 x(|x| < 1)tan−1 x1.2New notationSymbolMeaningThe indefinite integral of f(x) with respect to x i.e. a function whosederivative is f(x).Note thatacts like a pair of brackets around the function. Just as a left-hand bracket hasno meaning unless it is followed by a closing right-hand bracket, the integral sign cannot standby itself, but needs “dx” to complete it. The integral sign tells us what operation to performand the “dx” tells us that the variable with respect to which we are integrating is x.New termsAnti-derivativePrimitive functionIndefinite integralMeaningThese are all different ways of saying “a functionwhose derivative is ...”Merced Community College District, Merced College, 20162IntroductionThis booklet is intended for students who have never done integration before, or who havedone it before, but so long ago that they feel they have forgotten it all.Integration is used in dealing with two essentially different types of problems:The first type are problems in which the derivative of a function, or its rate of ... Purchase document to see full attachment

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