工程硕士入学考试网上辅导刘庆华数学讲义第三章一元函数积分学

2003.)(xfI,Ix∈∀)(xF)()(xfxF=′)(xF)(xf2.∫+=CxFdxxf)()(3.)(xfI4.)(xf1.[]∫∫∫±=±dxxgbdxxfadxxbgxaf)()()()(2.[])()(xfdxxf=′∫3.[]dxxfdxxfd)()(=∫4.CxFdxxF+=′∫)()(5.[]CxFxfd+=∫)()(6.∫∫=dxxfkdxxkf)()(2)(xF)(xf0,≠ba∫=+dxbaxf)(3+≥+=−0212101)(xexxxfx)(xf4)(xF)(xf)(xg)(xf)(xg)(xGA1)()(=′′xGxFB1)()(=′′xgxfC1))((=dxxfdGD1))((=dxxgdFB5xe1R+−≥−020xexexx-=xxxf01)(-)(xF)(xf)()()(aFbFdxxfba−=∫9[]baCf,∈)(xg[]ba,()ba,∈∃ξ∫∫=babadxxgfdxxgxf)()()()(ξ∫xadxxf)(∫xadttf)()()(xfdttfdxdxa=∫1=≠=0001sin)(2xxxxxf=≠−=′0001cos1sin2)(xxxxxxf201lim10=+∫∞→dxxxnx3∫=xadttfxF)()()(xf)(xF)(xf)(xF)(xfI0)(,,=∈∀∫βαβαdxxfIIxxf∈≡,0)(5∫∫2020)cos(sin)sin(sinππdxxdxx6∫−xdttxtfdxd022)(=7∫=tsdxtxftI0)(s8)(xf∫−=xxdttfxF)()(=′)(xF9ba,5sincoslim00=−+∫→xxxdtttaebx10()323232221limnnnnnn+++∞→1.Cexdxxfx+=∫22)()()(=xf2.xexf−=)(∫=dxxxf)(ln3.∫+=Cedxxfx22)(=)(xf4.∫+=Cxdxxf2)(∫=−dxxxf)1(25.)(xf1R[]=∫dxxfd)(6.)(xf1R[]=∫)(xfd7.CxFdxxf+=∫)()(∫=−−dxefexx)(8.{}2,1max)(xxf=1R1)0(=F+≤−+−+=1353111113131)(33xxxXxxxF9.∫→xxdtttx020coslim10.43sin02)(sin)(,0xxxgdttxfxx+==→∫ABCDC.)(),(xgxf0→x)(xf)(xg0→x∫=xtdttfxF0sin)()(∫=xtdtxG0tan)(ABCDA12.0)(≥xf∫∫∫===403202101)(tan,)(sin,)(ππdxxfIdxxfIdxxfI13.=∫xxdttdxd2)sin(cos14.∫∫+++xxtdttdt1020211=15.()nnnnnnn)()2)(1(1lim+++∞→1.∫dxxn2.∫xdx3.∫+21xdx4.∫dxax5.∫∫xdxxdxcossin1∫+dxxx32)15(2∫+dxex113∫+−dxxx32324∫+dxxx234∫−dxxxexx16∫xdxx2tan7∫xdxln8∫+dxxxxln1ln9∫xdxarctan10dxexexx∫+111)∫−232xdx2)∫+−222xdx3)∫−−1224xxxdx4)∫+−2243xxdxx5)∫+++)1)(1(2xxxxdx21)∫+dxxx2sin1cos2)∫+dxxxx23cos1cossin3)∫+−5cossin2xxdx4)∫xdxxcos5sin31)))cos,(sin)cos,sin(xxRxxR−=−)cos,(sin)cos,(sinxxRxxR−=−3))cos,(sin)cos,sin(xxRxxR=−−1∫−dxxa222∫−22axdx3∫+22axdx4∫−+dxbxax5Euler0azxacbxax+±=++20ccxzcbxax±=++2)())((221xxzxxxxa−=−−1)∫+++12xxxdx1.∫−dxxx42)5(2.∫−3)1(xxdxx3.dxx2sin1−4.∫−+dxxx13225.dxx321−6.∫−232xdx.∫+)1(xxdx8.∫21sinxdxx9.∫dxxx2ln10.∫xdxsin11.−=+++∫xxddxxdxxx1111124212.∫+xxxdxx44cossincossin13.∫+dxxx1214.∫−dxxx5215.∫++)2)(1(22xxdx16.∫−dxxx2117.∫dxxxsincos518.∫xdxarctan19.dxxx∫arcsin20.∫++dxxx)2)(1(21.∫−+25xxxdx22.∫+−232xxxdx23.∫+13xdx24.∫−+−2221)1(xxxxdx∫+23)1(N-L1∫−6123xxdx2∫eexdx1ln3∫−1022dxxx4dxxx∫441ln5+≥+=−0212101)(xexxxfx∫−11)(dxxf1.)(),(21xfxf[]ba,)()(21xfxf≤{})()(,),(21xfyxfbxayxD≤≤≤≤=[]∫−=badxxfxfA)()(121203xy=2xOy{}10,10),(≤≤≤≤=yxyxD)0(:≥=+ttyxl)(tSDl∫xdttS0)(≤−+−≤≤=212112211021)(22tttttttS2.{})(0,),(xfybxayxD≤≤≤≤=x[]∫=badxxfV2)(π{})(0,),(xfybxayxD≤≤≤≤=y∫=badxxfV)(2π3.4.()∈==βα,),(),(:ttyytxxL[][]∫∫′+′==babadttytxdsl22)()([]baxxfyL,),(:∈=[]∫∫′+==babadxxfdsl2)(1yxabf(x).{})(0,),(xfybxayxD≤≤≤≤=x[]∫∫′+==babadxxfxfdsxfA2)(1)(2)(2ππ()∈==βα,),(),(:ttyytxxLx[][]∫∫′+′==βαππdttytxtyydsA22)()()(226.1.2.