(高等数学英文课件)46-Substitution-in-Definite-Integrals

Chapter4Integration4.3EstimatingwithFiniteSums4.1IndefiniteIntegrals,DifferentialEquations,andModeling4.2IntegralRules,IntegrationbySubstitution4.4RiemannSumsandDefiniteIntegrals4.5TheMeanValueandFundamentalTheorems4.6SubstitutioninDefiniteIntegrals4.7NumericalIntegrationChapter4Integration4.3Esti14.6SubstitutioninDefiniteIntegrals4.6SubstitutioninDefiniteIn24.6.1SubstitutioninDefiniteIntegral4.6.2AreabetweenCurves4.6.1SubstitutioninDefinit3(高等数学英文课件)46-Substitution-in-Definite-Integrals4(高等数学英文课件)46-Substitution-in-Definite-Integrals5Solution1.Solution2.Solution1.Solution2.6Example.EvaluatetheintegralsSolution.Example.Evaluatetheintegral7Example.EvaluatetheintegralsSolution.Example.Evaluatetheintegral84.6.2AreabetweenCurves(曲线之间的平面图形面积)4.6.2AreabetweenCurves9(高等数学英文课件)46-Substitution-in-Definite-Integrals10Step1.Subdividetheinterval[a,b]intosubintervals.Step2.Selectsomenumberineachsubinterval,andthenobtainmanyrectangles.Step1.Subdividetheinterval11Step3.Takethesumofaboveproducts.Step4.TakethelimitationofRiemannsum.Step3.Takethesumofabove12Noticethatbothfandgarecontinuous.Therefore,wehaveNoticethatbothfandgarec13(高等数学英文课件)46-Substitution-in-Definite-Integrals14Solution.Solution.15Solution1.Solution1.16Solution2.DoesithasotherSolutions?Solution2.DoesithasotherS17Example.Evaluatetheareaoftheshaderegion.Example.Evaluatetheareaof18Example.Evaluatetheareaoftheshaderegion.Example.Evaluatetheareaof19Example.Evaluatetheareaoftheshaderegion.Example.Evaluatetheareaof20Example.Evaluatetheareaoftheshaderegion.Example.Evaluatetheareaof21Example.Evaluatetheareaoftheshaderegion.Example.Evaluatetheareaof22

ExercisesP3