% !TeX TXS-program:compile = txs:///arara % arara: pdflatex: {shell: yes, synctex: no, interaction: batchmode} \documentclass[a4paper,english,11pt]{article} \usepackage[margin=1cm,includefoot]{geometry} \usepackage[english]{tkz-grapheur} \usepackage{tcolorbox} \tcbuselibrary{skins,minted} \usepackage{babel} \begin{document} \part*{Integrals examples} \section{Below cruve, by default} \begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} \begin{GraphTikz}% [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] \DrawAxisGrids[Behind,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \DefineCurve[Name=ch]{0.25*(x+2)^2+1} \DrawIntegral% [Colors=blue/cyan,Style=fill]% {h(x)} %formula {-5.25}{1.5} \DrawCurve[Color=red]{h(x)} \DrawAxisGrids[Above,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \end{GraphTikz} \end{tcblisting} \section{Behind interpolation curve} \begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} \begin{GraphTikz}% [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \DefineLstInterpol{(-6,4)(-2,-2)(3,3.5)}[\interpoA] \DefineInterpoCurve[Name=interpotest,Tension=1.05]{\interpoA} \DrawIntegral% [NameInterpo=interpotest,Colors=blue/cyan,Style=fill,Type=itp,Tension=1.05]% {\interpoA} %pointsinterpo {-5.25}{1.5} \DrawInterpoCurve[Color=red,Tension=1.05]{\interpoA} \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \end{GraphTikz} \end{tcblisting} \section{Behind cubic spline} \begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} \begin{GraphTikz}% [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \DefineLstSpline{-6/4/-2§-5/2/-2§-4/0/-2§-2/-2/0§1/2/2§3/3.5/0.5}[\lstsplineA] \DefineSplineCurve[Name=splinetest]{\lstsplineA}<\SplineTeal> \DrawIntegral% [NameSpline=\SplineTeal,Type=spl,Colors=blue/purple,Style=hatch]% {splinetest} %namesplinecurve {-5}{2} \DrawSplineCurve[Color=teal]{\lstsplineA} \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \end{GraphTikz} \end{tcblisting} \section{Between curves} \begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} \begin{GraphTikz}% [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \DefineCurve[Name=ch]{0.25*(x+2)^2-1} \DefineCurve[Name=ck]{-0.25*x+1} \FindIntersections[Name=ITSC,Disp=false]{ch}{ck} \DrawIntegral% [Colors=olive/pink,Style=fill,Type=fct/fct,Bounds=node/abs]% {h(x)}[k(x)] %formules {(ITSC-1)}{1.5} \DrawCurve[Color=red]{h(x)} \DrawCurve[Color=blue]{k(x)} \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \end{GraphTikz} \end{tcblisting} \section{Between splines} \begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} \begin{GraphTikz}% [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \DefineLstSpline{-6/4/-2§-5/2/-2§-4/0/-2§-2/-2/0§1/2/2§3/3.5/0.5}[\lstsplineA] \DefineLstSpline{-6/-2/3§-2/4/0§3/-1/0}[\lstsplineB] \DefineSplineCurve[Name=splinetestolive]{\lstsplineA}<\SplineOlive> \DefineSplineCurve[Name=splinetestteal]{\lstsplineB}<\SplineTeal> \FindIntersections[Name=ITT,Disp=false]{splinetestteal}{splinetestolive} \DrawIntegral% [NameSpline=\SplineTeal,NameSplineB=\SplineOlive,Type=spl/spl,Colors=blue/purple,Bounds=nodes]% {splinetestolive} %Namecourbespline [splinetestteal] %Namecourbespline {(ITT-1)}{(ITT-2)} \DrawSplineCurve[Color=teal]{\lstsplineA} \DrawSplineCurve[Color=olive]{\lstsplineB} \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \end{GraphTikz} \end{tcblisting} \section{Between interpolations} \begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} \begin{GraphTikz}% [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \DefineLstInterpol{(-6,4)(-2,-2)(3,3.5)}[\interpoA] \DefineInterpoCurve[Name=interpotest]{\interpoA} \DefineLstInterpol{(-6,-2)(-1,4)(3,0)}[\interpoB] \DefineInterpoCurve[Name=interpotesta]{\interpoB} \DrawIntegral% [NameInterpo=interpotesta,NameInterpoB=interpotest,Type=itp/itp,Colors=olive/pink]% {\interpoB} %pointsinterpo [\interpoA] %pointsinterpo {-2}{1} \DrawInterpoCurve[Color=red]{\interpoA} \DrawInterpoCurve[Color=blue]{\interpoB} \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \end{GraphTikz} \end{tcblisting} \section{Betweend function and spline} \begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} \begin{GraphTikz}% [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \DefineCurve[Name=ch]{-0.25*(x+2)^2+3.5} \DefineLstSpline{-6/4/-2§-5/2/-2§-4/0/-2§-2/-2/0§1/2/2§3/3.5/0.5}[\lstsplineA] \DefineSplineCurve[Name=splineblue]{\lstsplineA}<\Splineblue> \DrawIntegral% [NameSplineB=\Splineblue,Type=fct/spl,Colors=olive/pink]% {h(x)} %formule [splineblue] %Namecourbespline {-3}{0} \DrawCurve[Color=red]{h(x)} \DrawSplineCurve[Color=blue]{\lstsplineA} \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \end{GraphTikz} \end{tcblisting} \section{Between spline and function} \begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} \begin{GraphTikz}% [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \DefineCurve[Name=ch]{0.25*(x+2)^2-2} \DefineLstSpline{-6/4/2§-5/-2/-2§-4/0/2§-2/2/0§1/-2/-2§3/3.5/-0.5}[\lstsplineA] \DefineSplineCurve[Name=splineblue]{\lstsplineA}<\Splineblue> \DrawIntegral% [NameSpline=\Splineblue,Type=spl/fct,Colors=olive/pink]% {splineblue} %Namecourbespline [h(x)] %formule {-3}{-1} \DrawCurve[Color=red]{h(x)} \DrawSplineCurve[Color=blue]{\lstsplineA} \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \end{GraphTikz} \end{tcblisting} \section{Between function and interpo} \begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} \begin{GraphTikz}% [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \DefineCurve[Name=cm]{-0.25*(x+2)^2+4} \DefineLstInterpol{(-6,4)(-5,-2)(-2,1)(1,-2)(3,3)}[\interpoB] \DefineInterpoCurve[Name=interpotestb]{\interpoB} \DrawIntegral% [NameInterpoB=interpotestb,Type=fct/itp,Colors=olive/pink]% {m(x)} %formule [\interpoB] %pointsinterpo {-4}{1} \DrawCurve[Color=red]{m(x)} \DrawInterpoCurve[Color=blue]{\interpoB} \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \end{GraphTikz} \end{tcblisting} \section{Between interpo and function} \begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} \begin{GraphTikz}% [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \DefineCurve[Name=courbeQ]{0.25*(x+2)^2-2.5} \DefineLstInterpol{(-6,-2)(-5,4)(-2,-1)(1,2)(3,-2)}[\interpoA] \DefineInterpoCurve[Name=interpotest]{\interpoA} \FindIntersections[Name=FGH,Disp]{interpotest}{courbeQ} \DrawIntegral% [NameInterpo=interpotest,Type=itp/fct,Colors=olive/pink,Bounds=nodes]% {\interpoA} %pointsinterpo [q(x)] %formule {(FGH-1)}{(FGH-2)} \DrawCurve[Color=red]{q(x)} \DrawInterpoCurve[Color=blue]{\interpoA} \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \end{GraphTikz} \end{tcblisting} \section{Between spline and interpo} \begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} \begin{GraphTikz}% [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \DefineLstSpline{-6/-2/2§-3/4/0§3/-2/0}[\lstsplineA] \DefineSplineCurve[Name=splinered]{\lstsplineA}<\Splinered> \DefineLstInterpol{(-6,4)(-5,-2)(-2,1)(1,-2)(3,3)}[\interpoB] \DefineInterpoCurve[Name=interpotestb]{\interpoB} \DrawIntegral% [NameInterpoB=interpotestb,NameSpline=\Splinered,Type=spl/itp,Colors=olive/pink]% {splinered} %Namecourbespline [\interpoB] %pointsinterpo {-4}{-2} \DrawSplineCurve[Color=red]{\lstsplineA} \DrawInterpoCurve[Color=blue]{\interpoB} \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \end{GraphTikz} \end{tcblisting} \section{Between interpo and spline} \begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} \begin{GraphTikz}% [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \DefineLstSpline{-6/4/-2§-3/-2.25/0§3/3/0}[\lstsplineB] \DefineSplineCurve[Name=splineblue]{\lstsplineB}<\Splineblue> \DefineLstInterpol{(-6,-2)(-5,4)(-2,-1)(1,2)(3,-2.5)}[\interpoA] \DefineInterpoCurve[Name=interpotest]{\interpoA} \FindIntersections[Name=UIO,Disp]{interpotest}{splineblue} \DrawIntegral% [NameInterpo=interpotest,NameSplineB=\Splineblue,Type=itp/spl,Colors=olive/pink,Bounds=nodes]% {\interpoA} %pointsinterpo [splineblue] %Namecourbespline {(UIO-1)}{(UIO-2)} \DrawSplineCurve[Color=blue]{\lstsplineB} \DrawInterpoCurve[Color=red]{\interpoA} \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} \end{GraphTikz} \end{tcblisting} \end{document}