Argthtjtr

How do I shade the region bound by the standard parabola and the square root function?

documentclass{amsart}

usepackage{amsmath}



usepackage{tikz}

usetikzlibrary{calc,intersections}







usepackage{pgfplots}

pgfplotsset{compat=1.11}







begin{document}



raisebox{0mm}[0mm][0mm]

{

begin{tikzpicture}

begin{axis}[width=2.25in, height=2.25in, axis equal image, axis on top, clip=false,

    axis lines=middle,

    xmin=-2,xmax=4, domain=-2:4,

    ymin=-0.75,ymax=4,

    restrict y to domain=-0.75:4,

    xtick={empty},ytick={empty},

    axis lines=middle,

    axis line style={latex-latex},

    xlabel=textit{x},ylabel=textit{y},

    axis line style={shorten >=-12.5pt, shorten <=-12.5pt},

    xlabel style={at={(ticklabel* cs:1)}, xshift=12.5pt, anchor=north west},

    ylabel style={at={(ticklabel* cs:1)}, yshift=12.5pt, anchor=south west}

]



%The graphs of the square root function and the standard parabola are plotted.

addplot[samples=501, domain=-2:2] {x^2};

addplot[samples=501, domain=0:4] {sqrt(x)};





%Coordinate A is the point of tangency to the graph of the standard parabola, and B is the

%x-intercept of the tangent line.

coordinate (A) at (-15/8,225/64);

coordinate (B) at (-15/16,0);



%Coordinate P is the point of tangency to the graph of the square root function, and Q is

%the y-intercept of the tangent line.

coordinate (P) at (15/4,{sqrt(15/4)});

coordinate (Q) at (0,{1/4*sqrt(15)});



end{axis}





%A "pin" is drawn to A.

draw[draw=gray, shorten <=1mm, shorten >=1mm] (A) -- ($(A)!0.5cm!-90:(B)$) node[anchor=west, inner sep=0,  font=scriptsize]{makebox[0pt][r]{$y=x^{2}$}};



%A "pin" is drawn to P.

draw[draw=gray, shorten <=1mm, shorten >=1mm] (P) -- ($(P)!0.5cm!90:(Q)$);

node[anchor=north, inner sep=0, outer sep=0, font=scriptsize] at ($(P)!0.4cm!90:(Q)$){makebox[0pt][l]{$y=sqrt{x}$}};



end{tikzpicture}

}



end{document}

That's a standard task for the fillbetween library.

documentclass{amsart}

usepackage{amsmath}



usepackage{tikz}

usetikzlibrary{calc}







usepackage{pgfplots}

pgfplotsset{compat=1.11}

usepgfplotslibrary{fillbetween}





begin{document}



raisebox{0mm}[0mm][0mm]

{

begin{tikzpicture}

begin{axis}[width=2.25in, height=2.25in, axis equal image, axis on top, clip=false,

    axis lines=middle,

    xmin=-2,xmax=4, domain=-2:4,

    ymin=-0.75,ymax=4,

    restrict y to domain=-0.75:4,

    xtick={empty},ytick={empty},

    axis lines=middle,

    axis line style={latex-latex},

    xlabel=textit{x},ylabel=textit{y},

    axis line style={shorten >=-12.5pt, shorten <=-12.5pt},

    xlabel style={at={(ticklabel* cs:1)}, xshift=12.5pt, anchor=north west},

    ylabel style={at={(ticklabel* cs:1)}, yshift=12.5pt, anchor=south west}

]



%The graphs of the square root function and the standard parabola are plotted.

addplot[samples=501, domain=-2:2,name path=parabola] {x^2};

addplot[samples=501, domain=0:4,name path=root] {sqrt(x)};



addplot[red!10] fill between [of=parabola and root, soft clip={domain=0:1}];

%Coordinate A is the point of tangency to the graph of the standard parabola, and B is the

%x-intercept of the tangent line.

coordinate (A) at (-15/8,225/64);

coordinate (B) at (-15/16,0);



%Coordinate P is the point of tangency to the graph of the square root function, and Q is

%the y-intercept of the tangent line.

coordinate (P) at (15/4,{sqrt(15/4)});

coordinate (Q) at (0,{1/4*sqrt(15)});



end{axis}





%A "pin" is drawn to A.

draw[draw=gray, shorten <=1mm, shorten >=1mm] (A) -- ($(A)!0.5cm!-90:(B)$) node[anchor=west, inner sep=0,  font=scriptsize]{makebox[0pt][r]{$y=x^{2}$}};



%A "pin" is drawn to P.

draw[draw=gray, shorten <=1mm, shorten >=1mm] (P) -- ($(P)!0.5cm!90:(Q)$);

node[anchor=north, inner sep=0, outer sep=0, font=scriptsize] at ($(P)!0.4cm!90:(Q)$){makebox[0pt][l]{$y=sqrt{x}$}};



end{tikzpicture}

}



end{document}