Argthtjtr

I am trying to generate a shaded area between three curves: two are
y=±√x and third one is y=5.

documentclass[10pt,multi=False,border=5pt,tikz,class=scrartcl]{standalone}

usepackage{xcolor}



usepackage{pgfplots}

pgfplotsset{compat=newest}

usetikzlibrary{arrows.meta}

usetikzlibrary{patterns}

usepgfplotslibrary{fillbetween}

begin{document}

begin{tikzpicture}

  begin{axis}[grid=both, axis equal=false, ymin=-1, ymax=6, xmin=-30, xmax=30,

    minor tick num=1,axis lines = middle,

    label style={font=small,at={(ticklabel cs:1.1)}},

    tick label style={font=footnotesize}]

    addplot [thick,dashed,samples=50, domain=-30:0,name path=p1] {sqrt(abs(x))};

    addplot [thick,samples=50, domain=0:30,name path=p2] {sqrt(abs(x))};

    addplot [thick,dashed,name path=p3] coordinates {(-25,5) (25,5)};

    path [name path=left, intersection segments={of=p1 and p3,sequence=L2 -- R1}];

    path [name path=right, intersection segments={of=p2 and p3,sequence=L1 -- R2}];

    addplot [pattern=north east lines,pattern color=blue,opacity=.8] fill between [

        of=left and right,reverse=false];

    draw [fill=gray,opacity=.5] (0,3.5) ellipse [x radius=12.25, y radius=.1];

    addplot+ [only marks,mark=*] coordinates { (-25,5) (25,5)}

        node [pos=0,above right] {footnotesizetextcolor{blue}{$B=(-25,5)$}}

        node [pos=1,above left] {footnotesizetextcolor{blue}{$A=(25,5)$}};

    node [right] at (11,3) {$r=x=y^2$};

  end{axis}

end{tikzpicture}

end{document}

Big thanks to Sigur for explaining the question to me! The issue is that the paths do not have the appropriate orientation. So I had to reorder the sequences and reverse one to get

documentclass[10pt,multi=False,border=5pt,tikz,class=scrartcl]{standalone}

usepackage{xcolor}



usepackage{pgfplots}

pgfplotsset{compat=newest}

usetikzlibrary{arrows.meta}

usetikzlibrary{patterns}

usepgfplotslibrary{fillbetween}

begin{document}

begin{tikzpicture}

  begin{axis}[grid=both, axis equal=false, ymin=-1, ymax=6, xmin=-30, xmax=30,

    minor tick num=1,axis lines = middle,

    label style={font=small,at={(ticklabel cs:1.1)}},

    tick label style={font=footnotesize}]

    addplot [thick,dashed,samples=50, domain=-30:0,name path=p1] {sqrt(abs(x))};

    addplot [thick,samples=50, domain=0:30,name path=p2] {sqrt(abs(x))};

    addplot [thick,dashed,name path=p3] coordinates {(-25,5) (25,5)};

    path [name path=left,  intersection segments={of=p1 and p3,sequence={R1[reverse] -- L2}}];

    path [name path=right, 

    intersection segments={of=p2 and p3,sequence={L1 -- R2}}];

    addplot [pattern=north east lines,pattern color=blue,opacity=.8] fill between [

        of=left and right,reverse=false];

    draw [fill=gray,opacity=.5] (0,3.5) ellipse [x radius=12.25, y radius=.1];

    addplot+ [only marks,mark=*] coordinates { (-25,5) (25,5)}

        node [pos=0,above right] {footnotesizetextcolor{blue}{$B=(-25,5)$}}

        node [pos=1,above left] {footnotesizetextcolor{blue}{$A=(25,5)$}};

    node [right] at (11,3) {$r=x=y^2$};

  end{axis}

end{tikzpicture}

end{document}

How can one debug this? Just draw these paths with arrows.

documentclass[10pt,multi=False,border=5pt,tikz,class=scrartcl]{standalone}

usepackage{xcolor}



usepackage{pgfplots}

pgfplotsset{compat=newest}

usetikzlibrary{arrows.meta}

usetikzlibrary{patterns}

usepgfplotslibrary{fillbetween}

begin{document}

begin{tikzpicture}

  begin{axis}[grid=both, axis equal=false, ymin=-1, ymax=6, xmin=-30, xmax=30,

    minor tick num=1,axis lines = middle,

    label style={font=small,at={(ticklabel cs:1.1)}},

    tick label style={font=footnotesize}]

    addplot [thick,dashed,samples=50, domain=-30:0,name path=p1] {sqrt(abs(x))};

    addplot [thick,samples=50, domain=0:30,name path=p2] {sqrt(abs(x))};

    addplot [thick,dashed,name path=p3] coordinates {(-25,5) (25,5)};

    path [name path=left, thick,draw=blue,-latex,

    intersection segments={of=p1 and p3,sequence=L2 -- R1}];

    path [name path=right, thick,draw=red,-latex,

    intersection segments={of=p2 and p3,sequence=L1 -- R2}];

    addplot [pattern=north east lines,pattern color=blue,opacity=.8] fill between [

        of=left and right,reverse=false];

    draw [fill=gray,opacity=.5] (0,3.5) ellipse [x radius=12.25, y radius=.1];

    addplot+ [only marks,mark=*] coordinates { (-25,5) (25,5)}

        node [pos=0,above right] {footnotesizetextcolor{blue}{$B=(-25,5)$}}

        node [pos=1,above left] {footnotesizetextcolor{blue}{$A=(25,5)$}};

    node [right] at (11,3) {$r=x=y^2$};

  end{axis}

end{tikzpicture}

end{document}

This reveals that the left path is a loop, which explains the faint dots on the left. It is a loop because you run through the curved part from top left to bottom right and then through the horizontal part.

This also shows that the horizontal curve is not at all necessary here, for the fills, you could just do

documentclass[10pt,multi=False,border=5pt,tikz,class=scrartcl]{standalone}

usepackage{xcolor}



usepackage{pgfplots}

pgfplotsset{compat=newest}

usetikzlibrary{arrows.meta}

usetikzlibrary{patterns}

usepgfplotslibrary{fillbetween}

begin{document}

begin{tikzpicture}

  begin{axis}[grid=both, axis equal=false, ymin=-1, ymax=6, xmin=-30, xmax=30,

    minor tick num=1,axis lines = middle,

    label style={font=small,at={(ticklabel cs:1.1)}},

    tick label style={font=footnotesize}]

    addplot [thick,dashed,samples=50, domain=-30:0,name path=p1] {sqrt(abs(x))};

    addplot [thick,samples=50, domain=0:30,name path=p2] {sqrt(abs(x))};

    addplot [thick,dashed,name path=p3] coordinates {(-25,5) (25,5)};

    path [name path=left, %thick,draw=blue,-latex,

    intersection segments={of=p1 and p3,sequence=L2}];

    path [name path=right, %thick,draw=red,-latex,

    intersection segments={of=p2 and p3,sequence=L1}];

    addplot [pattern=north east lines,pattern color=blue,opacity=.8] fill between [

        of=left and right,reverse=false];

    draw [fill=gray,opacity=.5] (0,3.5) ellipse [x radius=12.25, y radius=.1];

    addplot+ [only marks,mark=*] coordinates { (-25,5) (25,5)}

        node [pos=0,above right] {footnotesizetextcolor{blue}{$B=(-25,5)$}}

        node [pos=1,above left] {footnotesizetextcolor{blue}{$A=(25,5)$}};

    node [right] at (11,3) {$r=x=y^2$};

  end{axis}

end{tikzpicture}

end{document}

to get the first output above.

in your particular cae you can define single path for curve sqrt(abs(x)) and with this somehow simplify diagram code:

documentclass[margin=3.141592]{standalone}

usepackage{pgfplots}

pgfplotsset{compat=1.16}

usepgfplotslibrary{fillbetween}

usetikzlibrary{intersections, patterns}



begin{document}

begin{tikzpicture}[lbl/.style={font=footnotesize,text=blue}]

  begin{axis}[grid,

    %axis equal=false,

    xmin=-30,   xmax=30,

    ymin=-.5,   ymax=6,

    minor tick num=1,

    axis lines = middle,

    tick label style={inner sep=2pt, font=footnotesize},

    %

    every axis plot post/.append style={thick},

    samples=100

                ]

    addplot [draw=none,domain=-30:30,

                        name path=p1] {sqrt(abs(x))};

    addplot [dashed,   name path=p3,

              every mark/.append style={solid,scale=1.2},

              mark=*]   coordinates   {(-25,5) (25,5)}

                        node [pos=0,lbl, above right] {$B=(-25,5)$}

                        node [pos=1,lbl, above  left] {$A=( 25,5)$};

    addplot [pattern=north east lines,

              pattern color=blue,opacity=.8]

             fill between [of=p1 and p3];

    %

    addplot [dashed,domain=-30:0] {sqrt(abs(x))};

    addplot [       domain= 0:30] {sqrt(abs(x))};

    draw [fill=gray,opacity=.5] (0,3.5) ellipse [x radius=12.25, y radius=.1];

    node [right] at (11,3) {$r=x=y^2$};

  end{axis}

end{tikzpicture}

end{document}

which gives: