How to draw areas between curves of the form $x=f(y)$ and $x=g(y)$?

Question

I want to shade the region between two curves whose equations are of the form $x=f(y)$ and $x=g(y)$, where $f(y)\leq g(y)$ for all $y\in [c,d]$. I heard that pgfplots can be used. Also, the fillbetween library doesn't load in my Mac. Can you help me with this, guys? I want something like this one:

I used GeoGebra to generate the image. Thanks a lot!

Answer 1

Here is a suggestion using the fillbetween library and soft clip to domain y:

\addplot[thick,name path=P] ({.5*(x-2)^2+.5},{x})node[pos=0.92,above]{x=f(y)};
\addplot[thick,name path=Q]({-.3*(x-2)^2+2},{x})node[pos=0.94,above]{x=g(y)};
\addplot[red!80!black!40] fill between [of=P and Q, soft clip={domain y=\C:\D},reverse=true];

Code:

\documentclass[margin=5mm]{standalone}

\usepackage{lmodern} 
\usepackage{pgfplots}
\pgfplotsset{compat=1.10}% version 1.10 of pgfplots is needed
\usepgfplotslibrary{fillbetween}

\newcommand\C{}
\newcommand\D{}

\begin{document}
\begin{tikzpicture}
  \begin{axis}[
      xmin=-.5,xmax=3,
      axis lines*=middle,
      xtick=\empty,
      ytick=\empty,
      height=10cm,
      samples=200,
    ]
    \def\C{1}
    \def\D{3}
    \addplot[thick,name path=P] ({.5*(x-2)^2+.5},{x})node[pos=0.92,above]{x=f(y)};
    \addplot[thick,name path=Q]({-.3*(x-2)^2+2},{x})node[pos=0.94,above]{x=g(y)};
    \addplot[red!80!black!40] fill between [of=P and Q, soft clip={domain y=\C:\D},reverse=true];
    \draw({rel axis cs:0,0}|-{axis cs:0,\C})--({rel axis cs:1,1}|-{axis cs:0,\C});
    \draw({rel axis cs:0,0}|-{axis cs:0,\D})--({rel axis cs:1,1}|-{axis cs:0,\D});
    \node[above left]at(axis cs:0,\C){c};
    \node[above left]at(axis cs:0,\D){d};
    \node at (axis cs:1.25,2){R};
  \end{axis}
\end{tikzpicture}
\end{document}

Answer 2

Here's something to get you started, which uses the fillbetween library mentioned in the comments:

% arara: pdflatex
% !arara: indent: {overwrite: yes, localSettings: yes}
\documentclass{standalone}

% graphs
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}

% arrow style
\tikzset{>=stealth}

\begin{document}

% $x = y^2-4y$, $x = 2y-y^2$

\begin{tikzpicture}
    \begin{axis}[
            axis x line=middle,
            axis y line=middle,
            xlabel={$x$},
            ylabel={$y$},
            axis line style={<->},
            xmin=-5,xmax=5,
            ymin=-4,ymax=8,
            xtick={-4,-2,...,2,4},
            ytick={-2,2,4,6},
            minor xtick={-3,-1,...,3},
            minor ytick={-3,-1,...,7},
            grid=both,
            samples=100,
        ]
        \addplot[name path=A,domain=0:3]({x^2-4*x},{x});
        \addplot[name path=B,domain=0:3,ultra thick] ({2*x-x^2},{x});
        \addplot[fill=blue!50] fill between[of=A and B];
        \addplot[domain=-1:5,samples=50]({x^2-4*x},{x}) node[pos=.85,anchor=south] {$x=f(y)$};
        \addplot[domain=-1.4:3.4,samples=50,ultra thick] ({2*x-x^2},{x}) node[pos=.1,anchor=north] {$x=g(y)$};
    \end{axis}
\end{tikzpicture}

\end{document}

You'll see that I had to plot each curve twice - once for the shaded area, and once for the parts of the curves that go beyond the shaded area. You can certainly try plotting each curve just once, but the fill between part struggles (perhaps a guru has an improvement).

Here's another version that doesn't use the fillbetween library - very much the same idea, but perhaps not quite as nice with the result.

% arara: pdflatex
% !arara: indent: {overwrite: yes, localSettings: yes}
\documentclass{standalone}

% graphs
\usepackage{pgfplots}

% arrow style
\tikzset{>=stealth}

\begin{document}

% $x = y^2-4y$, $x = 2y-y^2$

\begin{tikzpicture}
    \begin{axis}[
            axis x line=middle,
            axis y line=middle,
            xlabel={$x$},
            ylabel={$y$},
            axis line style={<->},
            xmin=-5,xmax=5,
            ymin=-4,ymax=8,
            xtick={-4,-2,...,2,4},
            ytick={-2,2,4,6},
            minor xtick={-3,-1,...,3},
            minor ytick={-3,-1,...,7},
            grid=both,
            samples=100,
            axis on top,
        ]
        \addplot[domain=-1:5,samples=50]({x^2-4*x},{x});
        \addplot[domain=-1.4:3.4,samples=50,ultra thick] ({2*x-x^2},{x});
        \addplot[-,fill=red!50,domain=0:3,samples=50]({x^2-4*x},{x});
        \addplot[-,fill=red!50,domain=0:3,samples=50,thick]({2*x-x^2},{x});
    \end{axis}
\end{tikzpicture}

\end{document}