二重积分（double integral）

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1、二重积分（doubleintegral）In1Riemann-mathematicianInthefirstsection,theconceptsandpropertiesofdoubleintegralInthesecondsectionofdoubleintegralcalculationDefinitionofdoubleintegralconceptandnatureinthe2.inthe2.doubleintegralconceptandpropertyconceptandnatureinthe1.1.intheintroductionoft

2、heconceptandpropertiesofdoubleintegraldoubleintegraldoubleintegralintheapplicationof26.16.1thirddaydoubleintegraloftheintroductionofthedoubleintegralTheconceptandpropertiesofthedoubleintegralin3.in3.ofthe3,6.1doubleintegraldoubleintegralwithastereoitsbottomisxOyplaneboundedclosed

3、regionDissideboundaryinCregionoftheDbuslineandparalleltotheZaxisofthecylinder(LlineparalleltothelineandmovealongthefixedcurveCofatrackcalledCcalledcylindricalfixedcurvelinearcylinderalignmentLcalledcylinderbus)ontopofitisacontinuousfunctionoftwovariables(x,y)z=fexpressedbysurface

4、andAndf(x,y)=0thisstereocalledcylinder(page6.1.1Two)practicalproblemsnowrequirethevolume.1.thecylinderintothedoubleintegral(1)cylindervolume46.1.15flatcolumnishighwiththeformulav=constantapparatuscanitssize(height*bottomarea)calculation.Butthecylindertopisacurvedtheheightofz=f(x,

5、y)isavariablethevolumecannotbedirectlyfromtheaboveformula.Butinz=f(x,y)Disacontinuousfunctionontheandbottomareaandsmallcasesitsheightissmallchangethecylinderapproximatelyasflatcylinder.Thereforeofcylinderwecanbesimilartotheareaforcurvedtrapezoidwith"segmentation,approximate,summi

6、ngandlimit"Themethodforitssize.Thespecificmeasuresareasfollows:6firstwithagroupofDcurvenetworkwillbedividedintonsmallclosedarea...,andsmallclosedareaisrecordedas...RespectivelytothesesmallclosedareaTheboundarycurvelineforcylindricalparalleltotheZaxisofthebussoputtheentirecylinder

7、intontopcolumn.1dittyIn2inNin1in2inNinsecondcommunityineachdomainanypointastothebottomareaoffunctionvalueofFishighapproximatelyIofthevolumeofthecolumntopXiaoquvalueF,andtheapproximatecylindervolumevalue)(II,fromIIinin(II).From)(II,from(III),frominINIIIFfromin(17),fromexergyexergy

8、exergyinin).(Lim1.ZeroINIIfFinally,whent