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30:with(plots):with(plottools):" }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 
201 "> " 0 "" {MPLTEXT 1 204 36 "fI:=t->4/(1+t^2):aI:=0:bI:=1:NI:=20:"
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=-10:bJ:=10:NJ:=20:" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 0 ""
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" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 22 "Trapeze:=proc(f,a,b
,N)" }{MPLTEXT 1 204 11 "\nlocal i,S;" }{MPLTEXT 1 204 6 "\nS:=0;" }
{MPLTEXT 1 204 23 "\nfor i from 1 to N-1 do" }{MPLTEXT 1 204 22 "\n S:
=S+f(a+i*(b-a)/N);" }{MPLTEXT 1 204 4 "\nod;" }{MPLTEXT 1 204 30 "\nS:
=(S+(f(a)+f(b))/2)*(b-a)/N;" }{MPLTEXT 1 204 5 "\nend:" }{MPLTEXT 1 
204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "" }}}{EXCHG 
{PARA 201 "> " 0 "" {TEXT 206 11 "Question b)" }{MPLTEXT 1 207 0 "" }}
}{EXCHG {PARA 202 "" 0 "" {TEXT 208 21 "Calcul approch\351 de I " }
{TEXT 203 5 "avec " }{TEXT 208 13 "20 Rectangles" }{TEXT 203 3 " o\371
" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 22 "I=Int(fI(t),t=aI..b
I);" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#/^#\"\"\"-I$IntG6$I*protectedG
F)I(_syslibG6\"6$,$*$,&F%F%*$I\"tGF+\"\"#F%!\"\"\"\"%/F1;\"\"!F%" }
{TEXT 209 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 20 "I_(app
roch\351):=evalf(" }{MPLTEXT 1 204 7 "Trapeze" }{MPLTEXT 1 204 16 "(fI
,aI,bI,NI)); " }{MPLTEXT 1 204 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6
#>-I#I_G6\"6#I)approch|dyGF&$\"?4S2/ZMYGT&p)f<TJ!#H" }{TEXT 209 0 "" }
}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 37 " erreur:=evalf(abs(I_(
approch\351)-Pi));" }{MPLTEXT 1 204 0 "" }}{PARA 203 "" 1 "" {XPPMATH 
20 "6#>I'erreurG6\"$\";>VEg:]xkcjmmT!#H" }{TEXT 209 0 "" }}}{EXCHG 
{PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 202 "" 0 "" 
{TEXT 208 21 "Calcul approch\351 de J " }{TEXT 203 5 "avec " }{TEXT 
208 13 "20 Rectangles" }{TEXT 203 3 " o\371" }{TEXT 203 0 "" }}}
{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 27 "J=(Int(fJ(t),t=aJ..bJ))*
*2;" }{MPLTEXT 1 204 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#/I\"JG6\"
*$-I$IntG6$I*protectedGF*I(_syslibGF%6$-I$expGF)6#,$*$I\"tGF%\"\"#!\"
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{MPLTEXT 1 204 21 "J_(approch\351):=evalf((" }{MPLTEXT 1 204 7 "Trapez
e" }{MPLTEXT 1 204 20 "(fJ,aJ,bJ,NJ))**2); " }{MPLTEXT 1 204 0 "" }}
{PARA 203 "" 1 "" {XPPMATH 20 "6#>-I#J_G6\"6#I)approch|dyGF&$\"?P&)f9V
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{MPLTEXT 1 204 37 " erreur:=evalf(abs(J_(approch\351)-Pi));" }
{MPLTEXT 1 204 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#>I'erreurG6\"$
\";4-E]!o+J&eM1+l!#H" }{TEXT 209 0 "" }}}{EXCHG {PARA 201 "> " 0 "" 
{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {TEXT 206 11 "Questi
on c)" }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 
204 23 "Points_T:=proc(f,a,b,N)" }{MPLTEXT 1 204 11 "\nlocal i,S;" }
{MPLTEXT 1 204 9 "\nS:=NULL;" }{MPLTEXT 1 204 54 "\nfor i from 1 to N \+
do S:=S,[i/N,Trapeze(f,a,b,i)]; od;" }{MPLTEXT 1 204 5 "\n[S];" }
{MPLTEXT 1 204 5 "\nend;" }{MPLTEXT 1 204 0 "" }}{PARA 204 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 203 "" 1 "" {XPPMATH 20 "6#>I)Points_TG6\"f*
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9&F57#F1F%F%F%" }{TEXT 209 0 "" }}}{EXCHG {PARA 201 "> " 0 "" 
{MPLTEXT 1 204 29 "plot(Points_T(fI,aI,bI,50)); " }{TEXT 210 33 "Trac
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 I" }{MPLTEXT 1 204 0 "" }}{PARA 205 "" 1 "" {GLPLOT2D 400 400 400 
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+++++mFA$\"3+RP)zgR99$F37$$\"3[+++++++oFA$\"32#*QFy%[99$F37$$\"3a*****
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7$$\"3!**************R(FA$\"3yzbA54ZTJF37$$\"33+++++++wFA$\"3d\"=hMBx9
9$F37$$\"3E+++++++yFA$\"3(Gqdl2$[TJF37$$\"3U+++++++!)FA$\"3g5O#p[)[TJF
37$$\"3]*************>)FA$\"3(RFdi]$\\TJF37$$\"3o*************R)FA$\"3
R:GNr\")\\TJF37$$\"3')*************f)FA$\"3-Mjx9D]TJF37$$\"3-+++++++))
FA$\"3a'zNac1:9$F37$$\"3A+++++++!*FA$\"3T$Gj!\\.^TJF37$$\"3S+++++++#*F
A$\"3')fYi))Q^TJF37$$\"3Y*************R*FA$\"3%o*)oY?<:9$F37$$\"3k****
*********f*FA$\"3T#*pi:._TJF37$$\"3#)*************z*FA$\"3*fio!QK_TJF3
7$$\"\"\"F-$\"3Z`K#p)f_TJF3-%&COLORG6&%$RGBG$\"#5!\"\"$F-Fe[lFf[l-%+AX
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ot(Points_T(fJ,aJ,bJ,50)); " }{TEXT 210 33 "Trac\351 des points obtenu
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a+++++++cFC$\"3oc)z\\'QXs<F?7$$\"3g*************z&FC$\"3;KqXZQXs<F?7$$
\"3w**************fFC$\"3aw(4<&QXs<F?7$$\"3%**************>'FC$\"3[wps
]QXs<F?7$$\"39+++++++kFC$\"3;UK%4&QXs<F?7$$\"3I+++++++mFC$\"3=Gz*3&QXs
<F?7$$\"3[+++++++oFC$\"3%*op!4&QXs<F?7$$\"3a**************pFC$\"3?^_!4
&QXs<F?7$$\"3u*************>(FC$\"31ib!4&QXs<F?7$$\"3!**************R(
FC$\"3y3b!4&QXs<F?7$$\"33+++++++wFC$\"3A<b!4&QXs<F?7$$\"3E+++++++yFC$
\"3W:b!4&QXs<F?7$$\"3U+++++++!)FC$\"35;b!4&QXs<F?7$$\"3]*************>
)FC$\"3)e^04&QXs<F?7$$\"3o*************R)FCFbx7$$\"3')*************f)F
CF]x7$$\"3-+++++++))FCFbx7$$\"3A+++++++!*FCFbx7$$\"3S+++++++#*FC$\"3K;
b!4&QXs<F?7$$\"3Y*************R*FCFbx7$$\"3k*************f*FCF]x7$$\"3
#)*************z*FCF]x7$$\"\"\"F3Fcy-%&COLORG6&%$RGBG$F2!\"\"$F3FfzFgz
-%+AXESLABELSG6$Q!6\"F[[l-%%VIEWG6$;$\"16++++++SF*$\"&'>5!\"%;$!\"#Ffz
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{TEXT 212 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "" }}}
{EXCHG {PARA 201 "> " 0 "" {TEXT 206 11 "Question d)" }{MPLTEXT 1 204 
0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 22 "Suite_T:=proc(f,
a,b,N)" }{MPLTEXT 1 204 23 "\nlocal i,S,suite,delta;" }{MPLTEXT 1 204 
24 "\ndelta:=(b-a)/N;S:=NULL;" }{MPLTEXT 1 204 23 "\nfor i from 0 to N
-1 do" }{MPLTEXT 1 204 134 "\n S:=S,polygon([[a+i*delta,0],[a+(i+1)*de
lta,0],[a+(i+1)*delta,f(a+(i+1)*delta)],[a+i*delta,f(a+i*delta)]],colo
r=magenta,thickness=2);" }{MPLTEXT 1 204 4 "\nod;" }{MPLTEXT 1 204 3 "
\nS;" }{MPLTEXT 1 204 5 "\nend:" }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 
201 "> " 0 "" {MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 200 "" 0 "" {TEXT 
208 50 "Trac\351 des rectangels correspondant \340 l'int\351grale I" }
{TEXT 203 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 25 "TI:=Su
ite_T(fI,aI,bI,NI):" }{MPLTEXT 1 204 44 "GI:=plot(fI,aI..bI,color=blac
k,thickness=3):" }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" 
{MPLTEXT 1 204 22 "plots[display](TI,GI);" }{MPLTEXT 1 204 0 "" }}
{PARA 205 "" 1 "" {GLPLOT2D 758 400 400 {PLOTDATA 2 "69-%)POLYGONSG6%7
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H7$F($\"\"%F)-%&COLORG6&%$RGBG$\"#5!\"\"$F)F;F9-%*THICKNESSG6#\"\"#-F$
6%7&F*7$$\"?++++++++++++++5!#IF(7$FE$\"?SgRgRgRgRgRgRgRF1F.F5F=-F$6%7&
FD7$$\"?++++++++++++++:FGF(7$FO$\"?y()\\W-5^*z(4S/)>\"RF1FHF5F=-F$6%7&
FN7$$\"?++++++++++++++?FGF(7$FX$\"?:YQ:YQ:YQ:YQ:YQF1FQF5F=-F$6%7&FW7$$
\"?++++++++++++++DFGF(7$F[o$\"?HN#)eqk<THN#)eqkPF1FZF5F=-F$6%7&Fjn7$$
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\"?++++++++++++++SFGF(7$Ffp$\"?M5$z8C<b'*o?'eF[MF1F_pF5F=-F$6%7&Fep7$$
\"?++++++++++++++XFGF(7$F_q$\"?SELSELSELSELSELF1FhpF5F=-F$6%7&F^q7$$F,
FGF(7$Fhq$\"?++++++++++++++KF1FaqF5F=-F$6%7&Fgq7$$\"?++++++++++++++bFG
F(7$F`r$\"?Hpf4]f!*o@Zus,rIF1FiqF5F=-F$6%7&F_r7$$\"?++++++++++++++gFGF
(7$Fir$\"?#)eqk<THN#)eqk<THF1FbrF5F=-F$6%7&Fhr7$$\"?++++++++++++++lFGF
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1);" }{MPLTEXT 1 204 27 "\nfor i from 1 to 2^(N-1) do" }{MPLTEXT 1 
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{MPLTEXT 1 214 48 "\nT:=T,(b-a)*((f(a)+f(b))/2+Dichot(f,a,b,i))/2^i;" 
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{EXCHG {PARA 200 "" 0 "" {TEXT 208 66 "Valeurs successives T1 , T2 , T
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