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1、13.2 Iterated IntegralsProblem IntroductionEvaluating(,),where D is the rectangle=,:,Definitionwhere D is the rectangleSuppose for the time being that f(x,y)0 on D so that we may interpret thedoubleintegralasthevolumeVofthesolidunderthesurface.=,:,(,)=(,)D(,)=(,)iterated integrals(,)Example 1Evaluat
2、e In the inner integration,y is a constant,so3201(23).xy dx dy+21(2333)yxy dx+=+Consequently,32301045(23)33.2xy dx dyy dy+=+=Example 2Evaluate 2310(23).xy dy dx+In the inner integration,x is a constant,so302762(23)xxy dy+=Thus,2321012745(23)6.22xy dy dxxdx+=+=Example 3Find the volume V of the solid under the surface =4 2 and over the rectangle =,:0 1,0 2.According to the geometry meaning of double integral,the volume is =(4 2)=0201(4 2)=024 33 01=024 13 =113 12202=163SummaryThe Definition of Iterated IntegralsEvaluating the double integral over rectangular regionsIteratedIntegrals