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SCIENCE&TECHNOLOGYINFORMATION2011NO.30SCIENCE&TECHNOLOGYINFORMATION1,1[1]:f(x)[a,b],g(x)[a,b]ab,[ab]dxxfbgdxxfagdxxgxfabbaòòò+=xx)()()()()()((1):g(x),[a,b],a=x0x1x2xn=b;xk=xk-xk-1(k=1,2,,n)=max{x1xn}ò=badxxgxf)()(].,[,)()(lim1101kkxxknkkxxdxxfgkk-=®Îòå-xxlg(x))(1xg³)(2xg³)(ngx³0òòåò=££££-££xaxankxxbxabxadxufdxxfduufkk)(sup)()(inf11òòò壣=££-££xabxaxxxankkbxaduufgdxxfgduufgkk)(sup)()()()(inf)(1111xxx0®l)()(1agg®x:òòò££££££xaxabxababxaduufagdxxgxfduufag)(sup)()()()(inf)(,0)(¹ag()(ag=0)òòò££££££xabxabaxabxaduufdxxgxfagduuf)(sup)()()(1)(infòxaduuf)([a,b]x:dxxfagdxxgxfbaaòò=x)()()()((2)G(x)=g(x)-g(b),g(x),G(x),(2):òòò-=-=xababadxxfbgagdxbgxgxfdxxGxf)()]()([)]()([)()()(òòò=-+=ababadxxfbgagdxxfbgdxxgxfx)()]()([)()()()(òò+badxxfbgdxxfagxx)()()()(Îx[ab]g(x)ab(1):()()(0)()(0)()bbaafxgxdxgafxdxgbfxdxξξ=++-∫∫∫g(x)[a,b],f(x)[a,b],,:f(x)[a,b],F(x)=dxxfxaò)(dxxgxfbaò)()(,)()(),()(xFxvxgxu==)()(dxxgxfbaò)()()(xgxdFxgba==ò)()(xdgxFbaò)()(xdgxFbaò=òbaxdgF)()(x=)]()([*)(agbgdxxfa-òx;=òòbabadxxfbgdxxgxf)()()()(=+-=--òòòòxxxaaabadxxfagdaxfdxxfbgdxxfagbg)()(])()()[()()]()([dxxfagdxxfbgabòò+xx)()()()(Îx[a,b]2,,4[4]:(1)f(x)[a,b],g(x)[a,b],RnÎ1³n,x],[baÎ,:()()()();bbafxgxdxnfbgxdxx=∫∫(3)(2)f(x)[a,b],g(x)[a,b],RnÎ1³n,x],[baÎ,:(4)(3)f(x)[a,b],g(x)[a,b],m,nRÎnm££1,f(x),[,]abx∈,:(5)f(x),[,]abh∈,:(6)3,,,3.11:f(x)[a,b],g(x)[a,b],a,b,[a,b]x,òò=babdxxfbgdxxgxfx)()()()(:0,(()()()()()bbaaxbtgbthtfxgxdxfbthtdt-=--==-∫∫h(t)(abt-0)(2):00()()(0)()()()(0)babbfbthtdthfbtdtgbfxdxbahhh---=-=-∫∫∫()()()()bbaabbfxgxdxgbfxdxxxh-=∫∫3.2(341000):,,::O172:A:1672-3791(2011)10(c)-0175-02(177)SCIENCE&TECHNOLOGYINFORMATION2011NO.30SCIENCE&TECHNOLOGYINFORMATION(1),,,,,56,,,,(2),,,,,,,,,,,(3),,,,,,,,4,,:100,()10%,10%,40%,40%,,,,,,,,,5,:,,;,,,[1].[M].:,2004.[2].[EB/OL].[3].[J].,2006,8.[4].[M].:,2008.:2,,2duuttudtu===:òòò==++x22sin212sinsin2)(2xcxxcxxuduxduuudtt2121(coscos)22xxxxx=-≤=3.33:10lim01nnxdxx→∞=+∫:1(),()1nfxgxxx==+g(x)[0,1],x:;011)1)(1(111101010→+≤++=+=+≤∫∫nndxxdxxxnnxx01lim10=+⇒∫∞→dxxxnn:,4,,,,,[1].()[M].:,1979:191207[2],.Bn()[M].:,1979:454455[3].[J].(),1998,15():3637[4].[J].(),2004,19(3):8385(175)
本文标题:浅析积分第二中值定理及应用_石桃
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