托马斯微积分课件4.4 Riemann Sums and Definite Integrals.ppt

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1、Chapter4Integration4.3EstimatingwithFiniteSums4.1IndefiniteIntegrals,DifferentialEquations,andModeling4.2IntegralRules,IntegrationbySubstitution4.4RiemannSumsandDefiniteIntegrals4.5TheMeanValueandFundamentalTheorems4.6SubstitutioninDefiniteIntegrals4.7NumericalIntegration4.4RiemannSumsandDefiniteI

2、ntegrals(黎曼和与定积分)4.4.1RiemannSums4.4.2DefiniteIntegrals4.4.3AreaUndertheGraphofaNonnegativeFunction4.4.4AverageValueofAnArbitraryContinuousFunctions4.4.5PropertiesofDefiniteIntegrals4.4.1RiemannSums(黎曼和)Step1.Subdividetheinterval[a,b]intosubintervals.Thewidthofthekthsubinterval:Step2.Selectsomenum

3、berineachsubinterval,andthenobtainmanyrectangles.Step3.Takethesumofaboveproducts.Riemannsumforfontheinterval[a,b]apartitionof[a,b]Thenormofpartition4.4.2DefiniteIntegrals(定积分)ThenotationofDefiniteIntegrals4.4.3AreaUndertheGraphofaNonnegativeFunction(非负函数曲线围成图形的面积)2.Itequalsto?1.Doesitexists?Exampl

4、e3.AreaunderthecurveSolution.Example.Findtheintegralexpressionofthefollowingregions.4.4.4AverageValueofAnArbitraryContinuousFunctions(连续函数的平均值)Example4.FindtheaveragevalueofonSolution.4.4.5PropertiesofDefiniteIntegrals(定积分的性质)=RightLeftDenotetheminimumvalueandthemaximumvalueoffbymandM,respectively

5、.Example.SupposethatfandgarecontinuousandExercisesP35018,19,20,26,28,34.