\documentclass{report}


\usepackage{tikz}
\usetikzlibrary{intersections}
%\usetikzlibrary{pgfplots.fillbetween} % LATEX and plain TEX
%\usetikzlibrary[pgfplots.fillbetween] % ConTEXt

\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween} % LATEX and plain TEX
%\usepgfplotslibrary[fillbetween] % ConTEXt


\begin{document}
\begin{tikzpicture}
\begin{axis}
\addplot[blue,name path=A,domain=0:1] {sqrt(x)};
\addplot[red, name path=B,domain=0:1] {sqrt(x/2)};
\addplot[gray] fill between[of=A and B];
\end{axis}
\end{tikzpicture}
\end{document}