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1、?1?,?,?,?f x()a bg x()a ba b?,?f xg x()()?g x()a bf x dxg x dxabab()()FF?),2,1(picxi?)()(xgxf?,babxxxxann?110?,1iiixx?5?11()()nniiiix()()iigf55iigxf55?:?:?ix?:?ic?2p?12sup(),sup()a x ba x bMg xMf x?,0?/1?122()p MM13?34?:?max1inix?,()()iiigfx551?:?,?,?,?f x()g x()f x dxg x dxabab()()FF?2?,?f x()g x()
2、a b()$%&2()$%&?FFFbababadxxgdxxfdxxgxf)()()()(?2,0,1)()(?xxgxf?2200()2,()2f x dxg x dx?FF?20()()2f x g x dx?F?()$%&2()$%&?FFFbababadxxgdxxfdxxgxf)()()()(3?cba,f x dxab()Ff x dxac()Ff x dxcb()Ff x dxf x dxf x dxabaccb()()()FFF?209?cba?FFF?cbbacadxxfdxxfdxxf)()()(Fbadxxf)(=?Fcadxxf)(FFF?bccacbdxxfdxxf
3、dxxf)()()(?4?xdx01Fx dx201F?xdx12Fx dx212F?()1221xdx?F?201xdxF?sin xdx02?F?xdx02?F?1?)1,0(?x2xx?xdx01Fx dx201F?)2,1(?x2xx?xdx01F?x dx201F?)1,2(?x?2)21(?x?)1,0(?x?22?x?()1221xdx?F?201xdxF?0?xxx?sinsin xdx02?F?xdx02?F?5?0?f x(),a bf x().0f x dxab()F?0?),(,0)(00baxxf?0)()(lim00?xfxfxx?0c?000(min,)ax bx
4、33?),(0033?xxx?cxf?)()baf x dx?F0()xaf x dx3?F00()xxf x dx33?F0()bxf x dx3?.F00()xxf x dx33?F2c03.?0()0f x?0 xa?0 xb?0)(?Fbadxxf,()0tata bf x dx/?F?,?F?tadxxftF)()(a b,),()(battftF?()0f t 60)(?Fbadxxf6?,?,?0?f x()a bfx dxab20()F?f x()a b 210?f x(),a b2()fx?,?a b2()0fx.7?)(xf,ba),(ba)()(22bfdxxfabbaa
5、?F?),(ba?5?0)(?5f?,2abaB?0?()fB?)()(22bfdxxfabbaa?F?,)(xfbB?(,)(,)ba b5B0?0)(?5f?8?)(t?,0a)(xf),(?0)(.xf?()$%&Fadttaf0)(1?Fadttfa0)(1?,0aattttnn?1100?,max,111iiiiniiiitttttt?:?:54?f?:?()$%&:niiiniiiatfatf11)()(5?5?0?4?()$%&Fadttaf0)(1?Fadttfa0)(1?9?f x()1,0 1,0?FF.100)()(dxxfdxxf?1,0?211FF.?10)()()1
6、(?dxxfdxxf?10,x?2,1x?0(1)()f x dx?F?1(1)()f x?12()(1)()f x dxf x?F?)()(21xfxf.FF.?10)()()1(?dxxfdxxf?100()()()Ff x dxf x dx?FF10()()()Fff x?Fdx0,1,50?10()()ff x dx5?F?()()()Fff?5?f0?5?()0F?.?()F?15?()0F?()F?(0)(1)0FF?,1,0?/?()0F?.?0?1,0(?tx?fFFF.?10100)()()(dttfdttfdxxf?10?Young?yf x?()?,)0?0)0(?fxf
7、y?1()?Fadxxf0)(10()bfy dyab?.F?ab?0,0?)(afb?,0aaxxxxnn?1100?),2,1,0()(nixfyii?byyyynn?1100?11,?:?:iiiiiiyyyxxx?:?:niiiiniiiiniiiniiiyyxxxyyyfxxf111111111)()()()(abyxyxnn?00?max1inix:?4?0?4?:?:niiiniiiyyfxxf1111)()(212?Fadxxf0)(F?bdyyf01)(?)(afb?Fadxxf0)(F?bdyyf01)(ab?100()()()abF af x dxfy dyab?FF?(
8、)()F af ab?()f Tb?0aT?()F aaT?()F a()F aaT?()0F T?()0F a.?)(afb?Fadxxf0)(F?bdyyf01)(ab?11?f x()fx()h?f xh()?,?a blim|()()|hhabfxf xdx?F00?,?fxh()?f xh()?a b0?3?f x(),33?ba?()f xM?),(33?bax?,?f x()a b01/?,?a bnP8banM1?16niiix1?:?),2,1(ninabxi?:?ban3?10,?n?)(xf,baaan?,bab bn?02M?12nM?111|()()|()()|()(
9、)iinnbxhhiaxiiiifxf xdxfxf xdxfhfx55?FF:?213?min,8bahnM13?i?1,iixx5?2111,iiiiiihxxxxx xi5?11,nbabaxaxbnn?11)()(?iiiiifhf55?F?bahdxxfxf|)()(|1111?:?22)(2)(10111nabxnniiiii?lim|()()|hhabfxf xdx?F00?12?,?f x()g x()a b(1)?Schwarz?FFF2?!#+,-bababadxxgdxxfdxxgxf)()()()(222(2)?Minkowski?212212212)()()()(FF
10、F?bababadxxgdxxfdxxgxf?t2()()0batf xg xdx?.F?22()batfx dx?F2()()batf x g x dx?F2()0bagx dx.F?FFF2?!#+,-bababadxxgdxxfdxxgxf)()()()(222?2?()()baf x g x dx?F?122()bafx dxF?122()bagx dxF?2()bafx dx?F2()()baf x g x dx?F2()bagx dxF?2()bafx dx?F?1222()bafx dxF?122()bagx dxF2()bagx dx?F?2142()()baf xg xdx?
11、F?2112222()()bbaafx dxgx dx-#+!?+!,FF?212212212)()()()(FFF?bababadxxgdxxfdxxgxf?13?,?f x()g x()a b0)(.xf0)(?xg?)(max)()(lim1xfdxxgxfbxanbann?F?,?a b0)(?xg0()mg xM?()max()a x bAff x5?0A?0A?)()(lim55fxfx?,?0A1/?,ba?0?,?5?,?x?0()Af xA1?111()()()()()bnnnnaAmfx g x dxA M1?Fba?n?1()nm?1?1()nM ba?1?0N0?Nn?.1()1nmA1?12()1nM baA1?Nn?.?12()()bnnaAfx g x dxA211?F?1()()2bnnafx g x dxA1?F?1lim()()max()bnnana x bf xg x dxAf x?F?215