{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Out put" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Time s" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {SECT 1 {PARA 4 "" 0 "" {TEXT 256 11 "Exercice 19" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 2 "1) " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, \+ the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 867 "int_approx:=proc(a,b,f,n)\nlocal int_rect, int_tra p, alpha , FONCTION, RECTANGLES,TRAPEZES,sommets_des_trapezes,sommets_ des_rectangles;\nalpha:=(b-a)/n; \nint_rect:=sum(alpha*f(a+k*alpha),k= 0..n); \nint_trap:=sum(alpha/2*(f(a+k*alpha)+f(a+(k+1)*alpha)),k=0..n- 1);\nprint( approximation_de_l_int\351grale_par_la_m\351thode_des_rect angles);\nprint(evalf(int_rect));\nprint( approximation_de_l_int\351gr ale_par_la_m\351thode_des_trapezes);\nprint(evalf(int_trap));\nprint(v aleur_exacte_de_l_int\351grale);\nprint(evalf(int(f(x),x=a..b)));\nsom mets_des_trapezes:=seq([a+k*(b-a)/n,f(a+k*(b-a)/n)],k=0..n-1);\nTRAPEZ ES:=plot([sommets_des_trapezes],color=green):\nsommets_des_rectangles: =seq([[a+k*(b-a)/n,f(a+k*(b-a)/n)],[a+(k+1)*(b-a)/n,f(a+k*(b-a)/n)]],k =0..n-1);\nRECTANGLES:=plot([sommets_des_rectangles]):\nFONCTION:=plot (f(x),x=a..b,color=black);\ndisplay(\{FONCTION,TRAPEZES,RECTANGLES\}) \nend proc;\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%+int_approxGf*6&%\" aG%\"bG%\"fG%\"nG6*%)int_rectG%)int_trapG%&alphaG%)FONCTIONG%+RECTANGL ESG%)TRAPEZESG%5sommets_des_trapezesG%7sommets_des_rectanglesG6\"F4C1> 8&*&,&9%\"\"\"9$!\"\"F;9'F=>8$-%$sumG6$*&F7F;-9&6#,&F>8%-FB6$,$*&#F;\"\"#F;*&F7F;,&FEF;-FF6#,&FF;F;F=-%&printG6#%enapproximation_de_l_int| dygrale_par_la_m|dythode_des_rectanglesG-F[o6#-%&evalfG6#F@-F[o6#%Yapp roximation_de_l_int|dygrale_par_la_m|dythode_des_trapezesG-F[o6#-Fao6# FO-F[o6#%=valeur_exacte_de_l_int|dygraleG-F[o6#-Fao6#-%$intG6$-FF6#%\" xG/Ffp;F8*-%$seqG6$7$,&FF=F;-FF6#F_qFgn>8)-%%plotG6 $7#Fjp/%&colorG%&greenG>8+-F\\q6$7$F^q7$,&FF=F;FaqFgn> 8(-Ffq6#7#F]r>8'-Ffq6%FdpFgp/Fjq%&blackG-%(displayG6#<%FjrFerFdqF4F4F4 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "g:=x->exp(-x^2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6#%\"xG6\"6$%)operatorG%&arrow GF(-%$expG6#,$*$)9$\"\"#\"\"\"!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 21 "int_approx(-1,2,g,6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%enapproximation_de_l_int|dygrale_par_la_m|dythode_des_rectangle sG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+bw`3h\"!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%=valeur_exacte_de_l_int|dygraleG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Cb!*G;!\"*" }}{PARA 13 "" 1 "" {GLPLOT2D 612 312 312 {PLOTDATA 2 "6,-%'CURVESG6$7(7$$!\"\"\"\"!$\"3MB Wr6WzyO!#=7$$!3++++++++]F-$\"3y[SrIy+)y(F-7$$F*F*$\"\"\"F*7$$\"3++++++ ++]F-F17$F5F+7$$\"3++++++++:!#<$\"3YV'=cC#*R0\"F--%'COLOURG6&%$RGBGF4$ \"*++++\"!\")F4-F$6$7$F'7$F/F+-FB6&FD$\"#5F)F4F4-F$6$7$F.7$F4F1-FB6&FD F4FNF4-F$6$7$F37$F8F5-FB6&FDFNFNF4-F$6$7$F77$F5F1-FB6&FDF4F4FN-F$6$7$F :7$F\\l!\\<%F-7$$!3C++Dcx6x()F-$\"3@&RPY+\"QGYF-7$$! 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