Math1003IntegralCalculusandModelling Semester2ExercisesforWeek32010 AssumedKnowledgeIntegralsofsimplefunctionssuchasxn(including1/x)(sinx)cosx,ex.Thesimplepropertiesofde,niteintegrals. Objectives (2a)Tobeableto
Math1003IntegralCalculusandModelling Semester2ExercisesandSolutionsforWeek52012 AssumedKnowledgeSketchingcurvesofsimplefunctions.Integralsofsimplefunctionssuchasxn(including1/x)(sinx)cosx,ex. Objectives (4a)Tounderstandandbeabletouseintegrationbypartstoevaluatede,niteintegrals.(4b)Tounderstandthataninde,niteintegra...
which you can practice based on the integration formulas mentioned in this article. When we speak about integration by parts, it is about integrating the product of two functions, say y = uv. Moreintegral calculusconcepts are given, so keep learning integralformulas to solve problems accurately....
Math1003IntegralCalculusandModelling Semester2ExercisesandSolutionsforWeek22012 AssumedKnowledgeSigmanotationforsums.Theideasofasequenceofnumbersandofthelimitofasequence.Sketchingarepresentativegraphofafunctiongivenaformulaorasetoftabulatedvalues. Objectives
Math1003IntegralCalculusandModelling Semester2ExercisesforWeek112012 AssumedKnowledgeIntegrationtechniques. Objectives (10a)Tobeabletosolvedifferentialequationsthatareseparable,linearorboth. (10b)Tobeabletoconstructandsolveequationsdescribingflowandmixingproblems. ...
Math1003IntegralCalculusandModelling Semester2ExercisesforWeek52012 AssumedKnowledgeSketchingcurvesofsimplefunctions.Integralsofsimplefunctions suchasx n (including1/x),sinx,cosx,e x . Objectives (4a)Tounderstandandbeabletouseintegrationbypartstoevaluatedefiniteintegrals. (4b)Tounderstandthatanindefiniteinte...
Math1003IntegralCalculusandModelling Semester2ExercisesforWeek62012 AssumedKnowledgeSimplepropertiesofthefunctionslnxande x ,includingtheir derivatives. Objectives (5a)Toknowandbeabletousethepropertiesofthelnfunction. (5b)Toknowandbeabletousethepropertiesoftheexpfunction. (5c)Toknowandbeabletousethepropertiesof...
Math1003IntegralCalculusandModelling Semester2ExercisesandSolutionsforWeek132012 AssumedKnowledge Objectives (12a)Tobeabletorewritetwocoupledfirst-orderdifferentialequationsasasinglesecond- orderdifferentialequation. (12b)Tobeabletosketchthesolutionsofsecond-orderdifferentialequationswithconstant coefficients...
Math1003IntegralCalculusandModelling Semester2ExercisesandSolutionsforWeek62012 AssumedKnowledgeSimplepropertiesofthefunctionslnxande x ,includingtheir derivatives. Objectives (5a)Toknowandbeabletousethepropertiesofthelnfunction. (5b)Toknowandbeabletousethepropertiesoftheexpfunction. (5c)Toknowandbeabletousethe...