\documentclass{standalone}
\standaloneconfig{border=2mm 2mm 2mm 2mm}
%maths
\usepackage{mathtools}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsfonts}
%tikzpicture
\usepackage{tikz}
\usepackage{scalerel}
\usepackage{pict2e}
\usepackage{tkz-euclide}
\usetikzlibrary{calc}
\usetikzlibrary{patterns,arrows.meta}
\usetikzlibrary{shadows}
\usetikzlibrary{external}
%pgfplots
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepgfplotslibrary{statistics}
\usepgfplotslibrary{fillbetween}
%colours
\usepackage{xcolor}
\begin{document}
\pgfplotsset{
standard/.style={
axis line style = thick,
trig format=rad,
enlargelimits,
axis x line=middle,
axis y line=middle,
enlarge x limits=0.15,
enlarge y limits=0.15,
every axis x label/.style={at={(current axis.right of origin)},anchor=north west},
every axis y label/.style={at={(current axis.above origin) },anchor=south east},
grid=both,
ticklabel style={font=\tiny, fill=white}
}
}
\begin{tikzpicture}
\begin{axis}[standard,
xtick={0.1,0.2,0.5,1},
ytick={0.1,0.2,0.5,1,2},
xticklabels={$0.1$,$0.2$,$0.5$,$1$},
yticklabels={$0.1$,$0.2$,$0.5$,$1$,$2$},
xlabel={ $x$},
ylabel={ $y$},
samples=1000,
xmin=0, xmax=1.3,
ymin=0, ymax=1.3]
\node[anchor=center, label=south west:$O$] at (axis cs:0,0){};
\addplot[name path=F, line width=0.3mm, blue, domain={0:2}]{sqrt(x)} node[pos=0.8, above left] {$C_f$};
\path[name path=xAxis] (axis cs: 0,0) -- (axis cs: 1,0);
\addplot[fill=black, fill opacity=0.2] fill between [of=xAxis and F, soft clip={domain=0.2:1}];
\node[anchor=center, label=south east:$A(x)$] at (axis cs:0.5,0.5){};
\end{axis}
\end{tikzpicture}
\end{document}
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