2011NO.29
,,,, ,,1821, Dx 00 ,, Dy 0 00 ,, ,:,1854,, 0 ,, ;, 0 , (), , ,, e(y)dy=f(x)dx,,, , E(y)=F(x)+C,Dz=e(y)Dy+o(Dy) 1 Dz=f(x)Dx+o(Dx),,dz=e(y)Dy=e(y)dy,dz=f(x)Dx=f(x)dx, 2 4 e(y)dy=dz=f(x)dx,,f(x)dx dx=Dx [7] ,, Dy=g(x)Dx+o(Dx)?g(x)Dx=dy F(x)+C,dy=Dy,, g
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2.,
,,, ,, , 0 ,,, ,, 0 n b limf(x)DxdyP(xy) () ii,fxdx,,
n?¥= a [, i=1 dxQ(xy) f(x)Dxf(x)dx?,f(x)Dx dx=Dx iiii P(xy)=Q(xy)=0], n n , limf(x)Dxlimf(x)dx ii f(x)dxii Dx?0dx?0 i=1i=1
n n b b limf(x)dx=f(x)dxlim ,ii,,
a dx?0dx?0 a i=1i=1 6 f(x)dx , , , , n b[3] , limf(x)dx f(x)dx ii,
dx?0 a i=1
nn 1 n111
lim=lim=dx ¥ 2222 b0 nn?¥?¥ n++knx1 kk==11??k
f(x)Dxf(x)dx
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a [1].()[M].:,2011. i=1 n ?? n [2],.[M].:, b limf(x)dx=f(x)dx ,ii,
2005. dx?0a i=1 ,[3].RiemanmLebesgue dx?0dx 3.,,, dx[J].,1999,8(3):9598. ,[4].[J]., dx ,,1992,24(3):99102 , [5].[J]., ,2009,39(11):211216. [6]. ,, [J].,1994,18(11):9396. [7].[M].,1999. [8].[M].:,2010. 5 [9],[M].:,2002. , [3] ,: , 1821
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