input courbes.mp; verbatimtex %&latex \documentclass{article} \begin{document} \def\vect#1{\vec #1} etex beginfig(1); path p[],q[],t[]; repere(0,0,-1,3,-1,2,1cm,2cm); p1 = r_point(0,0)--r_point(0,1)--r_point(1,1)--r_point(1,0)--cycle; fill p1 withcolor 0.5*white; label.bot(btex $I$ etex, r_point(1,0)); label.rt(btex $K$ etex, r_point(1,1)); label.lft(btex $J$ etex, r_point(0,1)); label.bot(btex $\vect{i}$ etex, r_point(0.5,0)); label.lft(btex $\vect{j}$ etex, r_point(0,0.5)); label(btex $u.a.$ etex, r_point(0.5,0.5)); %trace du repère r_axes; r_origine; %r_unites; %r_labelxy; r_fin; endfig; %======================================================================== vardef fx(expr t) = t enddef; vardef fy(expr t) = cos(t)+4 enddef; %======================================================================== vardef gx(expr t) = t enddef; vardef gy(expr t) = cos(t-0.5)+3 enddef; %======================================================================== beginfig(2); path p[],q[],t[]; repere(0,0,-1,9,-1,6,1cm,1cm); %definition de la surface p1 = f_courbe(fx,fy,2,9,100); p2 = f_courbe(gx,gy,2,9,100); q1 = rx_droite(3); q2= rx_droite(8); q3 = r_droitedir(0,0,0); %remplissage de la surface t1 = buildcycle(q1,p1,q2,q3); fill t1 withcolor .8white; t2= buildcycle(q1,p2,q2,q3); unfill t2; fill t2 withcolor .4white; %trace de la surface draw p1;draw p2; draw r_point(3,0)--f_point(fx,fy,3); draw r_point(8,0)--f_point(fx,fy,8); label.lft(btex $y=f(x)$ etex, f_point(fx,fy,2)); label.lft(btex $y=g(x)$ etex, f_point(gx,gy,2)); label.bot(btex $a$ etex, r_point(3,0)); label.bot(btex $b$ etex, r_point(8,0)); %trace du repère r_axes; r_origine; %r_unites; %r_labelxy; r_fin; endfig; %======================================================================== vardef fx(expr t) = t enddef; vardef fy(expr t) = cos(t)+0.5 enddef; %======================================================================== vardef gx(expr t) = t enddef; vardef gy(expr t) = cos(t-0.5)-0.5 enddef; %======================================================================== beginfig(3); path p[],q[],t[]; repere(0,0,-1,9,-3,3,1cm,1cm); %trace du repère r_axes; r_origine; %r_unites; %r_labelxy; %definition de la surface p1 = f_courbe(fx,fy,2,9,100); p2 = f_courbe(gx,gy,2,9,100); q1 = rx_droite(3); q2= rx_droite(7); q3 = r_droitedir(0,0,0); %remplissage de la surface t1 = buildcycle(p2,q1,p1,q2); fill t1 withcolor .4white; %trace de la surface draw p1;draw p2; draw r_point(3,0)--f_point(gx,gy,3); draw r_point(7,0)--f_point(fx,fy,7); label.ulft(btex $y=f(x)$ etex, f_point(fx,fy,2)); label.lft(btex $y=g(x)$ etex, f_point(gx,gy,2)); label.top(btex $a$ etex, r_point(3,0)); label.bot(btex $b$ etex, r_point(7,0)); r_fin; endfig; %======================================================================== vardef fx(expr t) = t enddef; vardef fy(expr t) = cos(t)+4 enddef; %======================================================================== beginfig(4); path p[],q[],t[]; repere(0,0,-1,9,-1,6,1cm,1cm); %definition de la surface p1 = f_courbe(fx,fy,2,9,100); q1 = rx_droite(3); q2= rx_droite(6); q3 =rx_droite(8); q4 = r_droitedir(0,0,0); %remplissage de la surface t1 = buildcycle(q2,p1,q3,q4); fill t1 withcolor .4white; t2= buildcycle(q1,p1,q2,q4); fill t2 withcolor .9white; %trace de la surface draw p1; draw r_point(3,0)--f_point(fx,fy,3); draw r_point(6,0)--f_point(fx,fy,6); draw r_point(8,0)--f_point(fx,fy,8); label.lft(btex $y=f(x)$ etex, f_point(fx,fy,2)); label.bot(btex $a$ etex, r_point(3,0)); label.bot(btex $b$ etex, r_point(6,0)); label.bot(btex $c$ etex, r_point(8,0)); %trace du repère r_axes; r_origine; %r_unites; %r_labelxy; r_fin; endfig; %========================================================================= beginfig(5); path p[],q[],t[]; repere(0,0,-1,9,-1,8,1cm,1cm); %definition de la surface p1 = f_courbe(fx,fy,2,9,100); q1 = rx_droite(3); q3 =rx_droite(8); q4 = r_droitedir(0,0,0); %remplissage de la surface t1 = buildcycle(q1,p1,q3,q4); fill t1 withcolor .4white; %trace de la surface draw p1; draw r_point(3,0)--r_point(3,6); draw r_point(8,0)--r_point(8,6); draw r_point(0,6)--r_point(8,6); draw r_point(8,2)--r_point(0,2); label.lft(btex $y=f(x)$ etex, f_point(fx,fy,2)); label.bot(btex $a$ etex, r_point(3,0)); label.bot(btex $b$ etex, r_point(8,0)); label.ulft(btex $A$ etex, r_point(3,0)); label.urt(btex $B$ etex, r_point(8,0)); label.ulft(btex $F$ etex, r_point(3,2)); label.urt(btex $E$ etex, r_point(8,2)); label.top(btex $D$ etex, r_point(3,6)); label.top(btex $C$ etex, r_point(8,6)); label.lft(btex $M$ etex, r_point(0,6)); label.lft(btex $m$ etex, r_point(0,2)); %trace du repère r_axes; r_origine; %r_unites; %r_labelxy; r_fin; endfig; %======================================================================== beginfig(6); path p[],q[],t[]; repere(0,0,-1,9,-1,6,1cm,1cm); %definition de la surface p1 = f_courbe(fx,fy,2,9,100); q1 = rx_droite(3); q2= rx_droite(6); q3 =rx_droite(8); q4 = r_droitedir(0,0,0); %remplissage de la surface t1 = buildcycle(q1,p1,q3,q4); fill t1 withcolor .4white; %trace de la surface draw p1; draw r_point(3,0)--r_point(3,fy(7)); %draw r_point(7,0)--f_point(fx,fy,7) dashed evenly; draw r_point(0,fy(7))--r_point(3,fy(7)) dashed evenly; draw r_point(8,0)--r_point(8,fy(7)); draw r_point(3,fy(7))--r_point(8,fy(7)); label.lft(btex $y=f(x)$ etex, f_point(fx,fy,2)); label.bot(btex $a$ etex, r_point(3,0)); %label.bot(btex $c$ etex, r_point(7,0)); label.bot(btex $b$ etex, r_point(8,0)); label.lft(btex $h$ etex, r_point(0,fy(7))); %trace du repère r_axes; r_origine; %r_unites; %r_labelxy; r_fin; endfig; beginfig(7); numeric u; u=1cm; path p[],q[],c[]; %les axes et l'origine z0=(0u,0u); z1=(-3u,-3u); z2=(6u,0u); z3=(0u,10u); drawarrow z0--z1; drawarrow z0--z2; draw (0u,1u)--(0u,2u) dashed evenly ; draw (0u,4u)--(0u,5u) dashed evenly ; draw (0u,7u)--(0u,8u) dashed evenly ; draw (0u,0u)--(0u,1u); draw (0u,2u)--(0u,4u); draw (0u,5u)--(0u,7u); drawarrow (0u,8u)--(0u,10u); dotlabel.bot(btex $O$ etex, z0); label.lft(btex $x$ etex, z1); label.bot(btex $y$ etex, z2); label.lft(btex $z$ etex, z3); %les plans draw (-2u,1u)--(-1u,3u)--(6u,3u)--(5u,1u)--cycle; draw (-2u,4u)--(-1u,6u)--(6u,6u)--(5u,4u)--cycle; draw (-2u,7u)--(-1u,9u)--(6u,9u)--(5u,7u)--cycle; label.lft(btex $a$ etex, (0u,2u)); label.lft(btex $z$ etex, (0u,5u)); label.lft(btex $b$ etex, (0u,8u)); %le solide %le bas z10=(1u,2u); z11=(2u,2.8u); z12=(3u,2.5u); z13=(4u,2u); z14=(2u,1.3u); c1=z10{up}...{right}z11{right}...{right}z12{right}...{down}z13{down}...{left}z14{left}...cycle; fill c1 withcolor 0.5*white; draw c1; %le milieu z20=(1.5u,5u); z21=(2u,5.7u); z22=(3u,5.3u); z23=(3.5u,5u); z24=(2u,4.5u); c2=z20{up}...{right}z21{right}...{right}z22{right}...{down}z23{down}...{left}z24{left}...cycle; fill c2 withcolor 0.5*white; draw c2; %le haut z30=(1.5u,8u); z31=(2u,8.5u); z32=(3u,8.1u); z33=(3.5u,8u); z34=(2u,7.6u); c3=z30{up}...{right}z31{right}...{right}z32{right}...{down}z33{down}...{left}z34{left}...cycle; fill c3 withcolor 0.5*white; draw c3; %les generatrices q1 = z10...z20...z30; p1 = (-2u,4u)--(5u,4u); z40 = p1 intersectionpoint q1; draw z10...z40; draw z40...z20 dashed evenly; p2 = (-2u,7u)--(5u,7u); z41 = p2 intersectionpoint q1; draw z20...z41; draw z41...z30 dashed evenly; q2 = z13...z23...z33; z50 = p1 intersectionpoint q2; draw z13...z50; draw z50...z23 dashed evenly; z51 = p2 intersectionpoint q2; draw z23...z51; draw z51...z33 dashed evenly; q3 = z14...z24...z34; z60 = p1 intersectionpoint q3; draw z14...z60; draw z60...z24 dashed evenly; z61 = p2 intersectionpoint q3; draw z24...z61; draw z61...z34 dashed evenly; %surface label.rt(btex $S(z)$ etex, z23); endfig; %======================================================================== vardef fx(expr t) = t enddef; vardef fy(expr t) = cos(t) enddef; %======================================================================== vardef gx(expr t) = t enddef; vardef gy(expr t) = sin(t) enddef; %======================================================================== beginfig(8); path p[],q[],t[]; repere(0,0,-1,3,-1,2,1cm,1cm); %definition de la surface p1 = f_courbe(fx,fy,0,3.14/2,100); p2 = f_courbe(gx,gy,0,3.14/2,100); q1 = rx_droite(0); q2=rx_droite(3.14/2); %remplissage de la surface t1 = buildcycle(q1,p1,p2); fill t1 withcolor .4white; t2= buildcycle(p1,p2,q2); fill t2 withcolor .4white; %trace de la surface draw p1;draw p2; label.bot(btex $\frac{\pi}{2}$ etex, r_point(3.14/2,0)); %trace du repère r_axes; r_origine; %r_unites; %r_labelxy; r_fin; endfig; %======================================================================== vardef fx(expr t) = t enddef; vardef fy(expr t) = cos(t)+4 enddef; %======================================================================== beginfig(9); path p[],q[],t[]; repere(0,0,-1,9,-1,6,1cm,1cm); %definition de la surface p1 = f_courbe(fx,fy,2,9,100); q1 = rx_droite(3); q3 =rx_droite(8); q4 = r_droitedir(0,0,0); %remplissage de la surface t1 = buildcycle(q1,p1,q3,q4); fill t1 withcolor .4white; %trace de la surface draw p1; draw r_point(3,0)--f_point(fx,fy,3); draw r_point(8,0)--f_point(fx,fy,8); label.lft(btex $y=f(x)$ etex, f_point(fx,fy,2)); label.bot(btex $a$ etex, r_point(3,0)); label.bot(btex $b$ etex, r_point(8,0)); %trace du repère r_axes; r_origine; %r_unites; %r_labelxy; r_fin; endfig; %======================================================================== beginfig(10); pair x[],c[],p[]; repere(0,0,-1,7,-2,6,1cm,1cm); %on place les points x0=r_point(2,0); x1=r_point(2.5,0); x2=r_point(3.5,0); x3=r_point(5,0); x4=r_point(6,0); c1=r_point(0,1); c2=r_point(0,4); c3=r_point(0,-1); c4=r_point(0,3); p0=r_point(2,1); p1=r_point(2.5,1); p2=r_point(2.5,4); p3=r_point(3.5,4); p4=r_point(3.5,-1); p5=r_point(5,-1); p6=r_point(5,3); p7=r_point(6,3); %trace des rectangles draw x0--p0 dashed evenly; draw p0--c1 dashed evenly ; pickup pencircle scaled 1pt; draw p0--p1 ; pickup pencircle scaled 0.5pt; draw x1--p2 dashed evenly; draw p2--c2 dashed evenly ; pickup pencircle scaled 1pt; draw p2--p3; pickup pencircle scaled 0.5pt; draw p3--p4 dashed evenly; draw p4--c3 dashed evenly ; pickup pencircle scaled 1pt; draw p4--p5 ; pickup pencircle scaled 0.5pt; draw p5--p6 dashed evenly ; draw p6--c4 dashed evenly ; pickup pencircle scaled 1pt; draw p6--p7 ; pickup pencircle scaled 0.5pt; draw p7--x4 dashed evenly ; %label sur les axes label.lft(btex $c_{1}$ etex,c1); label.lft(btex $c_{2}$ etex,c2); label.lft(btex $c_{3}$ etex,c3); label.lft(btex $c_{4}$ etex,c4); label.llft(btex $x_{0}=a$ etex,x0); label.bot(btex $x_{1}$ etex,x1); label.bot(btex $x_{2}$ etex,x2); label.bot(btex $x_{3}$ etex,x3); label.bot(btex $x_{4}=b$ etex,x4); %trace du repère r_axes; r_origine; %r_unites; %r_labelxy; r_fin; endfig; %======================================================================== beginfig(11); pair x[],c[],p[]; repere(0,0,-1,7,-2,6,1cm,1cm); %on place les points x0=r_point(2,0); x1=r_point(2.5,0); x2=r_point(3.5,0); x3=r_point(5,0); x4=r_point(6,0); c1=r_point(0,1); c2=r_point(0,4); c3=r_point(0,-1); c4=r_point(0,3); p0=r_point(2,1); p1=r_point(2.5,1); p2=r_point(2.5,4); p3=r_point(3.5,4); p4=r_point(3.5,-1); p5=r_point(5,-1); p6=r_point(5,3); p7=r_point(6,3); %trace des rectangles pickup pencircle scaled 1pt; draw x0--p0 ; pickup pencircle scaled 0.5pt; draw p0--c1 dashed evenly ; pickup pencircle scaled 1pt; draw p0--p1 ; draw x1--p2 ; pickup pencircle scaled 0.5pt; draw p2--c2 dashed evenly ; pickup pencircle scaled 1pt; draw p2--p3; draw p3--p4 ; pickup pencircle scaled 0.5pt; draw p4--c3 dashed evenly ; pickup pencircle scaled 1pt; draw p4--p5 ; draw p5--p6 ; pickup pencircle scaled 0.5pt; draw p6--c4 dashed evenly ; pickup pencircle scaled 1pt; draw p6--p7 ; draw p7--x4 ; pickup pencircle scaled 0.5pt; %marque + ou - label(btex $+$ etex, 0.5*(x0+p1)); label(btex $+$ etex, 0.5*(x1+p3)); label(btex $-$ etex, 0.5*(x2+p5)); label(btex $+$ etex, 0.5*(x3+p7)); %label sur les axes label.lft(btex $c_{1}$ etex,c1); label.lft(btex $c_{2}$ etex,c2); label.lft(btex $c_{3}$ etex,c3); label.lft(btex $c_{4}$ etex,c4); label.llft(btex $x_{0}=a$ etex,x0); label.bot(btex $x_{1}$ etex,x1); label.bot(btex $x_{2}$ etex,x2); label.bot(btex $x_{3}$ etex,x3); label.bot(btex $x_{4}=b$ etex,x4); %trace du repère r_axes; r_origine; %r_unites; %r_labelxy; r_fin; endfig; %========================================================================== vardef fx(expr t) = t enddef; vardef fy(expr t) = t**2 enddef; %========================================================================== beginfig(12); %pour l'activite path p,q; numeric h; repere(0,0,-0.2,1.2,-0.2,1.2,10cm,10cm); %quadunite_x(1,black); %quadunite_y(1,black); r_axes; r_origine; r_unites; r_labelxy; p =f_courbe(fx,fy,0,1,100); draw p; trace_rectangles_min(fx,fy,0,1,1/5); trace_rectangles_max(fx,fy,0,1,1/5); r_fin; endfig; beginfig(13);%pour l'activite path p,q; numeric h; repere(0,0,-0.2,1.2,-0.2,1.2,10cm,10cm); %quadunite_x(1,black); %quadunite_y(1,black); r_axes; r_origine; r_unites; r_labelxy; p =f_courbe(fx,fy,0,1,100); draw p; trace_rectangles_min(fx,fy,0,1,1/10); trace_rectangles_max(fx,fy,0,1,1/10); r_fin; endfig; beginfig(14);%pour l'activite path p,q; numeric h; repere(0,0,-0.2,1.2,-0.2,1.2,10cm,10cm); %quadunite_x(1,black); %quadunite_y(1,black); r_axes; r_origine; r_unites; r_labelxy; p =f_courbe(fx,fy,0,1,100); draw p; trace_rectangles_min(fx,fy,0,1,1/20); trace_rectangles_max(fx,fy,0,1,1/20); r_fin; endfig; %======================================================================== vardef ix(expr t) = t enddef; vardef iy(expr t) = 1/t enddef; %======================================================================== beginfig(15); path p[],q[],t[]; repere(0,0,-0.2,1.2,-1,10,10cm,1cm); %definition de la surface p1 = f_courbe(ix,iy,0.01,1.2,100); q1 = rx_droite(0.4); q3 =rx_droite(1); q4 = r_droitedir(0,0,0); %remplissage de la surface t1 = buildcycle(q1,p1,q3,q4); fill t1 withcolor .4white; %trace de la surface draw p1; draw r_point(0.4,0)--f_point(ix,iy,0.4); draw r_point(1,0)--f_point(ix,iy,1); label.urt(btex $y=\frac{1}{x}$ etex, f_point(ix,iy,0.7)); label.urt(btex $\ln x {\textnormal{ si } 01}$ etex, r_point(1,3)); label.bot(btex $1$ etex, r_point(1,0)); label.bot(btex $x$ etex, r_point(1.8,0)); %trace du repère r_axes; r_origine; %r_unites; %r_labelxy; r_fin; endfig; end