{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "Times New Roman CE" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "Times New Roman CE" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "Times New Roman CE" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "Times New Roman CE" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "Times New Roman CE" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 261 "Times New Roman CE" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 4 "" 0 "" {TEXT 256 10 "P\370\355klad 4." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 13 " Vypo\350\355tejte " }{XPPEDIT 18 0 "Int(e^x*cos( x ),x= -1..1)" "6#-%$IntG6$*&)%\"eG%\"xG\"\"\"-%$cosG6#F)F*/F);,$F*!\"\"F*" } {TEXT -1 2 " ." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "plot(exp(x )*cos(x),x=-1..1,color=cyan,style=point,scaling=constrained); " }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6(-%'CURVESG6#7S7$ $!\"\"\"\"!$\"3wHTY.6m()>!#=7$$!3ommm;p0k&*F-$\"35\\'z\"[Z<:AF-7$$!3wK L$3$F-7$$!3\"omm T!R=0vF-$\"3!R&*RC`$z_MF-7$$!3u****\\P8#\\4(F-$\"37v;,'4k>t$F-7$$!3+nm ;/siqmF-$\"3r)>RR![-KSF-7$$!3[++](y$pZiF-$\"3+G!p)yi\\UVF-7$$!33LLL$ya E\"eF-$\"3/C$*z(*f`tYF-7$$!3hmmm\">s%HaF-$\"3a&o%GTruu\\F-7$$!3Q+++]$* 4)*\\F-$\"36Ta_pp:K7jo&F-7$$!31+++]1aZT F-$\"3h^WF!yA]/'F-7$$!3umm;/#)[oPF-$\"31iU[#))4)yjF-7$$!3hLLL$=exJ$F-$ \"3qWE(4R:^y'F-7$$!3*RLLLtIf$HF-$\"3xIzYykwOrF-7$$!3]++]PYx\"\\#F-$\"3 )>5ISX!p`vF-7$$!3EMLLL7i)4#F-$\"3za7[x04HzF-7$$!3c****\\P'psm\"F-$\"35 GIFOU$pM)F-7$$!3')****\\74_c7F-$\"3mR4V+po\\()F-7$$!3)3LLL3x%z#)!#>$\" 3Gj#*oBr'Q<*F-7$$!3KMLL3s$QM%Fdr$\"3!p_C&3O)ec*F-7$$!3]^omm;zr)*!#@$\" 3[6&Q:@G,***F-7$$\"3%pJL$ezw5VFdr$\"3E!zgrR!3V5!#<7$$\"3s*)***\\PQ#\\ \")Fdr$\"3!=9!G;XI\"3\"Fgs7$$\"3GKLLe\"*[H7F-$\"3#fpK\"z.HA6Fgs7$$\"3I *******pvxl\"F-$\"3?0VGz)GT;\"Fgs7$$\"3#z****\\_qn2#F-$\"38W8Fgs7$$\"3i******\\2goPF-$\"3! G$=@&z0aN\"Fgs7$$\"3UKL$eR<*fTF-$\"3]1GR@Of'Q\"Fgs7$$\"3m******\\)Hxe% F-$\"3Lo9jXO`=9Fgs7$$\"3ckm;H!o-*\\F-$\"3I%fcMV\\iW\"Fgs7$$\"3y)***\\7 k.6aF-$\"31[7\\%e$[s9Fgs7$$\"3#emmmT9C#eF-$\"3k]S\")=U5&\\\"Fgs7$$\"33 ****\\i!*3`iF-$\"3W\"=#R:)3_^\"Fgs7$$\"3%QLLL$*zym'F-$\"3<^U\"*Q*Q2`\" Fgs7$$\"3wKLL3N1#4(F-$\"3uW#=jiGBa\"Fgs7$$\"3Nmm;HYt7vF-$\"3=%Hpk$z6\\ :Fgs7$$\"3Y*******p(G**yF-$\"3Y'\\9mE^3b\"Fgs7$$\"3]mmmT6KU$)F-$\"3yt% HO%G1Z:Fgs7$$\"3fKLLLbdQ()F-$\"3SDl0+:Fgs7$$\"\"\"F*$\"3;&)e\"*RR po9Fgs-%&STYLEG6#%&POINTG-%'COLOURG6&%$RGBG$F*F*$\"*++++\"!\")Fd[l-%+A XESLABELSG6$Q\"x6\"Q!F[\\l-%(SCALINGG6#%,CONSTRAINEDG-%%VIEWG6$;F(Fgz% (DEFAULTG" 1 5 0 1 10 0 2 6 1 4 1 1.000000 45.000000 45.000000 0 0 "Cu rve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 81 "Zde je jedno, kterou f unkci budeme pova\236ovat za u a kterou za v'. Polo\236me tedy u=" } {XPPEDIT 18 0 "e^x" "6#)%\"eG%\"xG" }{TEXT -1 13 " a v'=cos x." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "I1 := Int(exp(x)*cos(x),x=0..Pi/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#I1G-%$IntG6$*&-%$expG6#%\"xG\"\"\"-%$cosGF+F-/F,;\" \"!,$%#PiG#F-\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "Pou\236ijem e metodu per-partes." }}{PARA 0 "" 0 "" {TEXT -1 10 "Nech\235 u = " } {XPPEDIT 18 0 "exp(x)" "6#-%$expG6#%\"xG" }{TEXT -1 7 " a v\264= " } {XPPEDIT 18 0 "cos(x)" "6#-%$cosG6#%\"xG" }{TEXT -1 2 " ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(student):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 29 "student[intparts](I1,exp(x));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,&-%$expG6#,$%#PiG#\"\"\"\"\"#F*-%$IntG6$*&-F%6# %\"xGF*-%$sinGF1F*/F2;\"\"!F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 258 135 "Nyn\355 nas tala situace, kdy vznikl\375 integr\341l nen\355 o nic jednodu\232\232 \355, ne\236 integr\341l p\371vodn\355. Op\354t pou\236ijeme metodu pe r-partes a to u\236it\355m u=" }{XPPEDIT 18 0 "e^x" "6#)%\"eG%\"xG" } {TEXT 259 1 "." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "student[intparts] (%,exp(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(-%$expG6#,$%#PiG#\"\" \"\"\"#F*F*!\"\"-%$IntG6$,$*&-F%6#%\"xGF*-%$cosGF3F*F,/F4;\"\"!F'F*" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 260 83 "Pokud z integr\341lu vytkneme -1, vznikl\375 integr\341l je \372pln\354 shodn\375 s p\371vodn\354 zadan\375m. " }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 25 "isolate(I1=expand(%),I1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$IntG6$*&-%$expG6#%\"xG\"\"\"-%$cosGF*F,/F+;\"\"!,$% #PiG#F,\"\"#,&*$-%%sqrtG6#-F)6#F3F,F4#F,F5!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 104 "Nyn\355 uk\341 \236eme, \236e Maple um\355 spo\350\355tat tento integr\341l p\370\355 mo, p\370edch\341zej\355c\355 v\375po\350ty popisuj\355 \"ru\350n\355 \" v\375po\350et" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "Int(exp (x)*cos(x),x=0..Pi/2)=int(exp(x)*cos(x),x=0..Pi/2);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#/-%$IntG6$*&-%$expG6#%\"xG\"\"\"-%$cosGF*F,/F+;\"\"!, $%#PiG#F,\"\"#,&-F)6#F2F4#F,F5!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }