二重积分的计算 (D是矩形区域)VIP免费

4.二重积分的计算(D是矩形区域)复习§§22：：平行截面面积为已知的立体的体积y0xzyabcdDD是矩形区域[a,b;c,d]z=f(x,y)baxy,xf)d(dcyyQ)d()(yQyyyxfz),(问题：Q(y)是什么图形？Q(y)=I是曲边梯形。Dyxy,xfId)d(.4.二重积分的计算(D是矩形区域)0xzyyabcdDdcbaxy,xfy)d(d.baxy,xf)d(Q(y)=dcyyQ)d(I同理，也可以先对y积分badcyyxfxId),(d..Dyxy,xfId)d(z=f(x,y)D是矩形区域[a,b;c,d]0xzycdDz=f(x,y))()()d,(yψyφxyxfx=(y)x=(y))(yQ.y问题：Q(y)是什么图形？Q(y)=D:(y)x(y)cydyyyxfz),(也是曲边梯形!5.二重积分的计算（D是曲线梯形区域）Dyxy,xfId)d(.dcyyQ)d(I=0xzyx=(y)ycdDdcyψyφxyxfy)())d,(d(.D:(y)x(y)cyd5.二重积分的计算（D是曲线梯形区域）.Dyxy,xfId)d()()()d,(yψyφxyxfdcyyQ)d(Q(y)=I=z=f(x,y)x=(y)D:x1(y)xx2(y)cydI=)()()d(yxyxxy,xf0yxx2(y)x1(y)DcdyDyxy,xfId)d(6.二重积分计算的两种积分顺序0yxcdyDx2(y)x1(y)I=6.二重积分计算的两种积分顺序.Dyxy,xfId)d()()()d(yxyxxy,xfD:x1(y)xx2(y)cyd0yxcdydcydDD:y1(x)yy2(x)axb0yxI=aby1(x)y2(x)Dx2(y)x1(y)x)()(d),(xyxyyyxfI=6.二重积分计算的两种积分顺序.Dyxy,xfId)d()()()d(yxyxxy,xfD:x1(y)xx2(y)cyd0yxcdyD0yxI=aby1(x)y2(x)Dx2(y)x1(y)x6.二重积分计算的两种积分顺序.Dyxy,xfId)d()()(d),(xyxyyyxfI=)()()d(yxyxxy,xfdcydD:x1(y)xx2(y)cydD:y1(x)yy2(x)axb0yxcdyD0yxI=aby1(x)y2(x)Dx2(y)x1(y)xbaxd6.二重积分计算的两种积分顺序.Dyxy,xfId)d()()(d),(xyxyyyxfI=)()()d(yxyxxy,xfdcydD:x1(y)xx2(y)cydD:y1(x)yy2(x)axb0yx2a2a24.将积分换序)d,(daaxxaxyyxfxIaD:axyxax解0x2aD1D2D3axy.yaax.yaax.DDDI)d,(daaaayxyxfy)d,(dayaaayxyxfy)d,(daayaaxyxfy.还有别的方法吗？0yx2a2aaD:axyxax解0x2aD1D2axyyaax.yaax.)d,(daaayxyxfy)d,(dayaayaaxyxfy.DDI24.将积分换序.)d,(daaxxaxyyxfxI