How to fill the limits of the two curves?

Question

I want to fill the limits of the two curves (as shown). This is my code

\documentclass[10pt]{article}
\usepackage{pgf,tikz}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
\definecolor{ttqqcc}{rgb}{0.2,0,0.8}
\definecolor{ffqqtt}{rgb}{1,0,0.2}
\definecolor{ttqqff}{rgb}{0.2,0,1}
\definecolor{uququq}{rgb}{0.25,0.25,0.25}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\draw[->,color=black] (-3.63,0) -- (3.67,0);
\foreach \x in {-3,-2,-1,1,2,3}
\draw[shift={(\x,0)},color=black] (0pt,2pt) -- (0pt,-2pt) node[below] {\footnotesize $\x$};
\draw[color=black] (3.48,0.07) node [anchor=south west] { $x$};
\draw[->,color=black] (0,-1.93) -- (0,5.57);
\foreach \y in {-1,1,2,3,4,5}
\draw[shift={(0,\y)},color=black] (2pt,0pt) -- (-2pt,0pt) node[left] {\footnotesize $\y$};
\draw[color=black] (0.06,5.19) node [anchor=west] { $y$};
\draw[color=black] (0pt,-10pt) node[right] {\footnotesize $0$};
\clip(-3.63,-1.93) rectangle (3.67,5.57);
\draw[color=ttqqff,fill=ttqqff,fill opacity=0.1, smooth,samples=50,domain=-1.7320508075688772:-1.0] plot(\x,{\x^4-4*\x^2+3}) -- (-1,0) -- (-1.73,0) -- cycle;
\draw[color=ffqqtt,fill=ffqqtt,fill opacity=0.1, smooth,samples=50,domain=-1.0:1.0] plot(\x,{\x^4-4*\x^2+3}) -- (1,0) -- (-1,0) -- cycle;
\draw[color=ttqqcc,fill=ttqqcc,fill opacity=0.1, smooth,samples=50,domain=1.0:1.7320508075688772] plot(\x,{\x^4-4*\x^2+3}) -- (1.73,0) -- (1,0) -- cycle;
\draw[smooth,samples=100,domain=-3.6342419080068153:3.665758091993186] plot(\x,{(\x)^4-4*(\x)^2+3});
\begin{scriptsize}
\fill [color=uququq] (-1.73,0) circle (1.5pt);
%\draw[color=uququq] (-1.87,-0.33) node {$A$};
\fill [color=uququq] (-1,0) circle (1.5pt);
%\draw[color=uququq] (-0.85,-0.35) node {$B$};
\fill [color=uququq] (1,0) circle (1.5pt);
%\draw[color=uququq] (1.1,0.25) node {$C$};
\fill [color=uququq] (1.73,0) circle (1.5pt);
%\draw[color=uququq] (1.84,0.25) node {$D$};
\end{scriptsize}
\end{tikzpicture}
\end{document}

I want the fill has the form Please help me.

Answer 1

The code provided produces this output in my system:

which shows some problem with negative values for the x-coordinate. I decided then to work only for positive values of the x-coordinate and then use a reflection. For the desired patterns, you can use the patterns library:

\documentclass[10pt]{article}
\usepackage{pgf,tikz}
\usetikzlibrary{arrows,patterns}
\pagestyle{empty}

\definecolor{ttqqcc}{rgb}{0.2,0,0.8}
\definecolor{ffqqtt}{rgb}{1,0,0.2}
\definecolor{ttqqff}{rgb}{0.2,0,1}
\definecolor{uququq}{rgb}{0.25,0.25,0.25}

\begin{document}

\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]

\draw[->] (-3.63,0) -- (3.67,0);
\foreach \x in {-3,-2,-1,1,2,3}
  \draw[shift={(\x,0)}] (0pt,2pt) -- (0pt,-2pt) 
    node[below] {\footnotesize $\x$};
\draw[color=black] (3.48,0.07) node [anchor=south west] { $x$};

\draw[->] (0,-1.93) -- (0,5.57);
\foreach \y in {-1,1,2,3,4,5}
  \draw[shift={(0,\y)}] (2pt,0pt) -- (-2pt,0pt) 
    node[left] {\footnotesize $\y$};
\draw[color=black] (0.06,5.19) node [anchor=west] { $y$};

\draw (0pt,-10pt) node[right] {\footnotesize $0$};

\clip(-3.63,-1.93) rectangle (3.67,5.57);
\draw[pattern color=ffqqtt,pattern=north east lines,fill opacity=0.1, smooth,samples=50,domain=0:1.0] 
plot(\x,{\x^4-4*\x^2+3}) -- (1,0) -- (0,0) -- cycle;
\draw[pattern color=ttqqcc,pattern=crosshatch,fill opacity=0.1, smooth,samples=50,domain=1.0:1.7320508075688772] 
plot(\x,{\x^4-4*\x^2+3}) -- (1.73,0) -- (1,0) -- cycle;

\begin{scope}[xscale=-1]
\draw[pattern color=ffqqtt,pattern=north east lines,fill opacity=0.1, smooth,samples=50,domain=0:1.0] 
  plot(\x,{\x^4-4*\x^2+3}) -- (1,0) -- (0,0) -- cycle;
\draw[pattern color=ttqqcc,pattern=crosshatch,fill opacity=0.1, smooth,samples=50,domain=1.0:1.7320508075688772] 
  plot(\x,{\x^4-4*\x^2+3}) -- (1.73,0) -- (1,0) -- cycle;
\end{scope}

\draw[smooth,samples=100,domain=-3.6342419080068153:3.665758091993186] plot(\x,{(\x)^4-4*(\x)^2+3});

\fill [color=uququq] (-1.73,0) circle (1.5pt);

\fill [color=uququq] (-1,0) circle (1.5pt);

\fill [color=uququq] (1,0) circle (1.5pt);

\fill [color=uququq] (1.73,0) circle (1.5pt);

\end{tikzpicture}
\end{document}

For this kind of plots, the pgfplots package seems a more natural choice:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{patterns}
\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
        xmin=-3,xmax=3,
        ymin=-1.5,ymax=5,
        axis on top] 
    \addplot[color=red,domain=-2.8:2.8,samples=100] {(\x)^4-4*(\x)^2+3};

    \addplot+[mark=none,
        domain=-1:1,
        samples=100,
        pattern=north east lines,
        pattern color=red]{(\x)^4-4*(\x)^2+3} \closedcycle;

    \addplot+[mark=none,
        domain=1:1.7320508075688772,
        samples=100,
        pattern=crosshatch,
        draw=red,
        pattern color=blue!60]{(\x)^4-4*(\x)^2+3} \closedcycle;    

    \addplot+[mark=none,
        domain=-1.7320508075688772:-1,
        samples=100,
        pattern=crosshatch,
        draw=red,
        pattern color=blue!60]{(\x)^4-4*(\x)^2+3} \closedcycle;    
    \end{axis}
\end{tikzpicture}

\end{document}

Answer 2

A short and simple solution with tkz-fct

\documentclass[10pt]{article}
\usepackage{tkz-fct}
\usetikzlibrary{arrows,patterns}
\pagestyle{empty}

\begin{document}

\begin{tikzpicture}[scale=1.5]
   \tkzInit[xmin=-3,xmax=3,ymin=-2,ymax=4]
   \tkzGrid
   \tkzAxeXY
   \tkzFct[domain = -2.2:2.2]{x**4-4*x**2+3}
   \tkzDrawArea[pattern=north west lines, pattern color=red!60,domain = -1:1] 
   \tkzDrawArea[pattern=north west lines, pattern color=blue!60,domain = 1.0:1.7320] 
   \tkzDrawArea[pattern=north west lines, pattern color=blue!60,domain = -1.7320:-1] 
   \tkzDefPointByFct[draw,ref=A](1)
   \tkzLabelPoint[above right](A){$x_1$}
   \tkzDefPointByFct[draw,ref=B](1.732)
   \tkzLabelPoint[above right](B){$x_2$}   
\end{tikzpicture}

\end{document} 

Answer 3

I'd do this using pgfplots as follows, note the use of styles

\documentclass{standalone}

\usepackage{pgfplots}
\usetikzlibrary{patterns}

% set style for the axis
\pgfplotsset{mystyle/.style={
                    axis x line=middle,
                    axis y line=middle,
                    axis on top,
                    }}

% set styles for the patterns
\pgfplotsset{first pattern/.style={pattern=crosshatch,pattern color=blue}}
\pgfplotsset{second pattern/.style={pattern=north east lines, pattern color=red}}

\begin{document}
\begin{tikzpicture}[/pgf/declare function={f=x^4-4*x^2+3;}]
    \begin{axis}[mystyle,
      xmin=-4,xmax=4,
      ymin=-2,ymax=6]
        \addplot[first pattern]expression[domain=-1.7320508:-1]{f}\closedcycle;
        \addplot[second pattern]expression[domain=-1:1]{f}\closedcycle;
        \addplot[first pattern]expression[domain=1:1.7320508]{f}\closedcycle;
        \addplot[<->,samples=100] expression[domain=-3:3]{f};
    \end{axis}
\end{tikzpicture}
\end{document}

Answer 4

Just 4 fun with PSTricks!

\documentclass[pstricks,border=5pt]{standalone}
\usepackage{pst-plot,pst-eucl}
\psset{saveNodeCoors}
\def\f{x 2 exp dup 4 sub mul 3 add}

\begin{document}
\begin{pspicture}(-2.5,-1)(2.5,4)
\psset{PointName=none,PointSymbol=none}
% Determine the intersection points
\pstInterFF{\f}{0}{-2}{A}
\pstInterFF{\f}{0}{-1}{B}
\pstInterFF{\f}{0}{1}{C}
\pstInterFF{\f}{0}{2}{D}
% Fill the bounded regions
\pscustom[fillstyle=solid,fillcolor=yellow!50]{\psplot{N-A.x}{N-D.x}{\f}\psline(!N-D.x 0)(!N-A.x 0)}
% Plot the curve
\psplot[plotpoints=100]{-2}{2}{\f}
% Draw the coordinate axes
\psaxes{->}(0,0)(-2.5,-1)(2.5,4)[$x$,-90][$y$,180]
% Draw the intersection points
\psdots(A)(B)(C)(D)
\end{pspicture}
\end{document}

Explanations:

• \psset{saveNodeCoors} is needed to allow us to use the node's x and y values out of the box. For example, if a node A has been defined then we can refer to its x value by invoking N-A.x. The prefix N- is mandatory even though it adds a bit complexity (at least for me)!
• \def\f{x 2 exp dup 4 sub mul 3 add} defines the function in Reverse Polish Notation (RPN). x 2 exp dup 4 sub mul 3 add represents x^4-4x^2+3. The expression uses stack operations that are a bit complicated for untrained human beings. However, you can learn it in several minutes to grasp the essence by googling "RPN".
• \psset{PointName=none,PointSymbol=none} is used to disable point labels and point symbols that are generated automatically by pst-eucl whenever you specify points (aka nodes).
• \pstInterFF{<function 1 in RPN>}{<function 2 in RPN>}{<starting point>}{<intersection point name>} will determine the intersection point between 2 functions (in RPN) near the starting point you specified.
• \pscustom[fillstyle=solid,fillcolor=yellow!50]{\psplot{N-A.x}{N-D.x}{\f}\psline(!N-D.x 0)(!N-A.x 0)} fill the bounded regions by the curve and the x axis.
• the remaining codes are self-explanatory.