**TI83F* AppVariable file 06/25/03, 20:35q ` INTGTXT` ^ G]ny$ygG@wC3w` " r  Integrals (Text)David Dude6/25/2003 v.1.0dude@dudefree.com00dx=PCPkkdx=Pkx+CPkxkxdx=Pkx---+C2P)x^nnxdx=Pn+1x------+Cn+1P,1/xdx--=xPln|x|+CP -e^kxkxedx=Pkxe----+CkP'b^xxbdx=Pxb-----+ClnbP "sin kxsin(kx)dx=P-cos(kx)-------+CkP "cos kxcos(kx)dx=Psin(kx)------+CkP 1sec x2secxdx=Ptanx+CP 0csc x2cscxdx=P-cotx+CP+sec x tan xsecxtanxdx=Psecx+CP+csc x cot xcscxcotxdx=P-cscx+CP tan xtanxdx=P-ln|cosx|+CP cot xcotxdx=Pln|sinx|+CP sec xsecxdx=Pln|secxtanx|+CP csc xcscxdx=P-ln|cscxcotx|+CP >sindx-------=(1-x)Psinx+CP Ccos-dx-------=(1-x)Pcosx+CP 6tandx-----=1+xPtanx+CP >cot-dx------=1+xPcotx+CP Hsecdx---------=|x|(x-1)Psecx+CP Dcsc-dx---------=|x|(x-1)Pcscx+CP ln xlnxdx=Pxlnx-x+CP !sin xsin xdx=P1-cos2x---------dx2P &cos xcos xdx=P1+cos2x---------dx2P tFundThm1FundamentalTheoremofCalculus,Part1:dx--f(t)dt=#dxaPf(x)P lFundThm2FundamentalTheoremofCalculus,Part2:bf(x)dx=#a*PF(b)-F(a)(whereFisanyantiderivativeoff)PPOrderOfIntOrderofIntegration:af(x)dx=bPb-f(x)dx=aP -a to aaf(x)dx=aP0PEConstMultConstantMultipleRule:kf(x)dx=Pkf(x)dxP-Sum/DiffRulef(x)+/-g(x)dxPf(x)dx+/-g(x)dxP}AdditivityAdditivityProperty:bcf(x)dx+f(x)dx=abPcf(x)dxaP (MaxMinMax-MinInequality:P(minf)(b-a)bf(x)dxa#*(maxf)(b-a)P 6AvgValAverageValueofaFunction:P1b----f(x)dxb-aaPLIntByPartsIntegrationbyPartsFormula:udv=Puv-vduP