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Die Fläche einer Region, die durch zwei Graphen begrenzt wird

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Die Fläche einer Region, die durch zwei Graphen begrenzt wird

Ich suche nach einem professionelleren Programm als dem hier unten. Ich glaube, ich kann die Kurven benennen und TiKz die Schnittpunkte berechnen lassen, anstatt sie mit Stift und Papier zu finden. Ich gebe zu, dass ich eine gute Stunde mit dieser Konstruktion verbracht habe. Entschuldigung für Redundanz oder überflüssige Kommentare.

\documentclass{article}
\usepackage{tikz}

\begin{document}
\begin{minipage}{.3\textwidth}
\begin{center}
\begin{tikzpicture}[scale=.5,declare function={g(\x)=(\x-1)^(2)+1;},declare 
        function={f(\x)=.5*\x+4;}]
\draw[fill=orange!40!white,dashed]
  plot[domain=-.6375:3.137,samples=167,variable=\x] ({\x},{f(\x)})
    -- (3.137,-2) -| cycle;
 \draw[fill=white,dashed]
   plot[domain=-.6375:3.137,samples=167,variable=\x] ({\x},{g(\x)})
    -- (3.137,-2) -| cycle; 
 \draw[domain=-1:3.8,smooth,variable=\x,red,<->,thick] plot ({\x},{g(\x)});
 \draw[domain=-1.4:4.4,smooth,variable=\x,blue,<->,thick] plot ({\x}, 
   {f(\x)});
 \draw[fill] (-.6375,{g(-.6375)}) circle (4pt);
 \draw[fill] (-.6375,-2) circle (4pt);
 \draw[fill] (3.137,{g(3.137)}) circle (4pt);
 \draw[fill] (3.137,-2) circle (4pt);
 %\draw[domain=-3:-1,smooth,variable=\x,red,<-,thick] plot ({\x},{g(\x)});
 \draw[dashed] (-.6375,{g(-.6375)})--(-.6375,-2) node[below] {$a$};
 \draw[dashed] (3.137,{g(3.137)})--(3.137,-2) node[below] {$b$};
 \draw (-2.25,-2)--(5,-2);
 \node at (3.8,{g(3.8)}) [right,text=red] {$g$};
 \node at (4.4,{f(4.4)}) [right,text=blue] {$f$};
 \node at (1,3) [] {$A$};           
 \end{tikzpicture}
 \end{center}
 \end{minipage}
 \hspace{1cm}
 \begin{minipage}{.3\textwidth}
 \begin{center}
 \begin{tikzpicture}[scale=.5,declare function={g(\x)=(\x-1)^(2)+1;},declare 
    function={f(\x)=.5*\x+4;}]
 \draw[fill=orange!40!white]
    plot[domain=-.6375:3.137,samples=167,variable=\x] ({\x},{f(\x)})
    -- (3.137,-2) -| cycle;
 %\draw[fill=white,dashed]
 %   plot[domain=-.6375:3.137,samples=167,variable=\x] ({\x},{g(\x)})
 %   -- (3.137,-2) -| cycle;    
 %\draw[domain=-1:3.8,smooth,variable=\x,red,<->,thick] plot ({\x},{g(\x)});
 \draw[domain=-1.4:4.4,smooth,variable=\x,blue,<->,thick] plot ({\x}, 
   {f(\x)});
 \draw[fill] (-.6375,{g(-.6375)}) circle (4pt);
 \draw[fill] (-.6375,-2) circle (4pt);
 \draw[fill] (3.137,{g(3.137)}) circle (4pt);
 \draw[fill] (3.137,-2) circle (4pt);
 %\draw[domain=-3:-1,smooth,variable=\x,red,<-,thick] plot ({\x},{g(\x)});
 \draw[] (-.6375,{g(-.6375)})--(-.6375,-2) node[below] {$a$};
 \draw[] (3.137,{g(3.137)})--(3.137,-2) node[below] {$b$};
 \draw (-2.25,-2)--(5,-2);
 \node at (3.8,{g(3.8)}) [right,text=white] {$g$};
 \node at (4.4,{f(4.4)}) [right,text=blue] {$f$};
 \node at (1,1) [] {$A_{2}$};           
 \end{tikzpicture}
 \end{center}
 \end{minipage}
 \hspace{1cm}
 \begin{minipage}{.3\textwidth}
 \begin{center}
 \begin{tikzpicture}[scale=.5,declare function={g(\x)=(\x-1)^(2)+1;},declare 
   function={f(\x)=.5*\x+4;}]
   %\draw[fill=white]
   %   plot[domain=-.6375:3.137,samples=167,variable=\x] ({\x},{f(\x)})
   %   -- (3.137,-2) -| cycle;
 \draw[fill=orange!40!white,dashed]
    plot[domain=-.6375:3.137,samples=167,variable=\x] ({\x},{g(\x)})
    -- (3.137,-2) -| cycle; 
  \draw[domain=-1:3.8,smooth,variable=\x,red,<->,thick] plot ({\x},{g(\x)});
  %\draw[domain=-1.4:4.4,smooth,variable=\x,blue,<->,thick] plot ({\x}, 
   {f(\x)});
 \draw[fill] (-.6375,{g(-.6375)}) circle (4pt);
 \draw[fill] (-.6375,-2) circle (4pt);
 \draw[fill] (3.137,{g(3.137)}) circle (4pt);
 \draw[fill] (3.137,-2) circle (4pt);
 %\draw[domain=-3:-1,smooth,variable=\x,red,<-,thick] plot ({\x},{g(\x)});
 \draw[] (-.6375,{g(-.6375)})--(-.6375,-2) node[below] {$a$};
 \draw[] (3.137,{g(3.137)})--(3.137,-2) node[below] {$b$};
 \draw (-2.25,-2)--(5,-2);
 \node at (3.8,{g(3.8)}) [right,text=red] {$g$};
 %\node at (4.4,{f(4.4)}) [right,text=] {$f$};
 \node at (1,1) [below] {$A_{1}$};          
 \end{tikzpicture}
 \end{center}
 \end{minipage}

\end{document}

Dies gibt aus:

Bildbeschreibung hier eingeben

Antwort1

pgfplotsDies ist ein Vorschlag, der die Bibliothek lädt und verwendet fillbetween, aber nur Ti hatkZ-Syntax. Sie müssen keine Schnittpunkte manuell berechnen.

Bildbeschreibung hier eingeben

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{backgrounds}
\begin{document}
\begin{minipage}{.3\textwidth}
\centering
\begin{tikzpicture}[scale=.5,declare function={g(\x)=(\x-1)^(2)+1;
        f(\x)=.5*\x+4;}]
 \draw[domain=-1.4:4.4,smooth,variable=\x,blue,<->,thick,name path=f1] plot ({\x}, 
   {f(\x)});
 \draw[domain=-1:3.8,smooth,variable=\x,red,<->,thick,name path=g1] plot ({\x},{g(\x)});
 \begin{scope}[on background layer]  
  \path[fill=orange!40!white,%blue,very thick,
   intersection segments={of=f1 and g1,sequence={A1 -- B1[reverse]}}]; 
 \end{scope} 
 \draw[fill,name intersections={of=f1 and g1,name=I1}] 
  (I1-1) circle (4pt) (I1-2) circle (4pt)
  (I1-1|-0,-2) circle (4pt) (I1-2|-0,-2) circle (4pt);
 \draw[dashed] (I1-1)--(I1-1|-0,-2) node[below] {$\mathstrut a$};
 \draw[dashed] (I1-2)--(I1-2|-0,-2) node[below] {$\mathstrut b$};
 \draw (-2.25,-2)--(5,-2);
 \node at (3.8,{g(3.8)}) [right,text=red] {$g$};
 \node at (4.4,{f(4.4)}) [right,text=blue] {$f$};
 \node at (1,3)  {$A$};           
 \end{tikzpicture}
\end{minipage}
\hspace{1cm}
\begin{minipage}{.3\textwidth}
\centering
\begin{tikzpicture}[scale=.5,declare function={g(\x)=(\x-1)^(2)+1;
        f(\x)=.5*\x+4;}]
 \draw[domain=-1.4:4.4,smooth,variable=\x,blue,<->,thick,name path=f2] plot ({\x}, 
   {f(\x)});
 \path[domain=-1:3.8,smooth,variable=\x,<->,name path=g2] plot ({\x},{g(\x)});
 \draw[fill,name intersections={of=f2 and g2,name=I2}] 
  (I2-1) circle (4pt) (I2-2) circle (4pt)
  (I2-1|-0,-2) circle (4pt) (I2-2|-0,-2) circle (4pt);
 \begin{scope}[on background layer]  
  \path[fill=orange!40!white]
  (I2-1|-0,-2) -- (I2-1) -- (I2-2) -- (I2-2|-0,-2); 
 \end{scope} 
 \draw (I2-1)--(I2-1|-0,-2) node[below] {$\mathstrut a$};
 \draw (I2-2)--(I2-2|-0,-2) node[below] {$\mathstrut b$};
 \draw (-2.25,-2)--(5,-2);
 \node at (3.8,{g(3.8)}) [right,text=white] {$g$};
 \node at (4.4,{f(4.4)}) [right,text=blue] {$f$};
 \node at (1,1) [] {$A_{2}$};           
 \end{tikzpicture}
\end{minipage}
\hspace{1cm}
\begin{minipage}{.3\textwidth}
\centering
 \begin{tikzpicture}[scale=.5,declare function={g(\x)=(\x-1)^(2)+1;
        f(\x)=.5*\x+4;}]
 \path[domain=-1.4:4.4,smooth,variable=\x,name path=f3] plot ({\x}, 
   {f(\x)});
 \draw[domain=-1:3.8,smooth,variable=\x,red,<->,thick,name path=g3] plot ({\x},{g(\x)});
 \draw[fill,name intersections={of=f3 and g3,name=I3}] 
  (I3-1) circle (4pt) (I3-2) circle (4pt)
  (I3-1|-0,-2) circle (4pt) (I3-2|-0,-2) circle (4pt);
 \path[name path=aux] (I3-1) -- (I3-1|-0,-2) -- (I3-2|-0,-2) -- (I3-2) -- cycle;
 \begin{scope}[on background layer]  
  \path[fill=orange!40!white,%blue,very thick,
   intersection segments={of=aux and g3,sequence={A0[reverse] -- B1}}]; 
 \end{scope} 
 \draw (I3-1)--(I3-1|-0,-2) node[below] {$\mathstrut a$};
 \draw (I3-2)--(I3-2|-0,-2) node[below] {$\mathstrut b$};
 \draw (-2.25,-2)--(5,-2);
 \node at (3.8,{g(3.8)}) [right,text=red] {$g$};
 \node at (1,1) [below] {$A_{1}$};          
\end{tikzpicture}
\end{minipage}
\end{document}

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