57 lines
1.8 KiB
Plaintext
57 lines
1.8 KiB
Plaintext
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// préambule asymptote
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usepackage("amsmath,amssymb");
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usepackage("inputenc","utf8");
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usepackage("icomma");
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import lib_jl;
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unitsize(1cm,1cm);
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real xmin=-5.5, ymin=-1.5, xmax=5.5, ymax=5.5;
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xlimits(xmin,xmax);
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ylimits(ymin,ymax);
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xaxis(BottomTop,xmin=xmin,xmax=xmax,Ticks("%",extend=true,Step=1),p=linewidth(0.5pt)+gray(0)+dotted);
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yaxis(LeftRight,ymin=ymin,ymax=ymax,Ticks("%",extend=true,Step=1),p=linewidth(0.5pt)+gray(0)+dotted);
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real F(real x) {return .5*(x+5)*(.5x^2+.25x+.5);}
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draw(graph(F,-6,4,n=400),linewidth(1pt)+deepred+solid);
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xlimits(xmin,xmax,Crop);
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ylimits(ymin,ymax,Crop);
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xaxis(axis=YEquals(0),xmin=xmin,xmax=xmax,Ticks("%",beginlabel=true,endlabel=true,begin=true,end=true,NoZero,Step=1,Size=1mm),p=linewidth(1pt)+black,Arrow(2mm),true);
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yaxis(axis=XEquals(0),ymin=ymin,ymax=ymax,Ticks("%",beginlabel=true,endlabel=true,begin=true,end=true,NoZero,Step=1,Size=1mm),p=linewidth(1pt)+black,Arrow(2mm),true);
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pair O=(0,0), I=(1,0), J=(0,1), A=(-4,0), B=(1,0), C=(-1.5,0);
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labelx(Label("$O$",NoFill), 0, SW);
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label("$I$",I,SE);
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label("$J$",J,NW);
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draw(line(A-(0,2),A+(0,2)),deepblue+pen1);
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label("$a$",A,SE,deepblue);
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path integrale1=buildcycle((A.x, F(A.x))--A--C--(C.x, F(C.x)),graph(F,A.x,C.x));
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add("integrale1",hatch(H=.5mm,dir=NE,lightred));
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fill(integrale1,pattern("integrale1"));
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label(scale(.9)*"$\int_{a}^{c} f(x)\; dx$",((A.x+C.x)/2,2),deepred);
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path integrale2=buildcycle((C.x, F(C.x))--C--B--(B.x, F(B.x)),graph(F,C.x,B.x));
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add("integrale2",hatch(H=.5mm,dir=NW,lightgreen));
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fill(integrale2,pattern("integrale2"));
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label(scale(.9)*"$\int_{c}^{b} f(x)\; dx$",((C.x+B.x)/2,.5),deepgreen);
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draw(line(B-(0,2),B+(0,2)),deepblue+pen1);
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label("$b$",B,SW,deepblue);
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draw(line(C-(0,2),C+(0,2)),deepgreen+pen1);
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label("$c$",C,SW,deepgreen);
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shipout(bbox(0.1cm,0.1cm,white));
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