Just sqrt(x) with 1,2,3,4 ticks

[karush]

\begin{tikzpicture}[scale=1]
%preamble \usepackage{pgfplots}
\begin{axis}[xmin=-1, xmax=5, ymin=-1, ymax=3, axis lines=middle, ticks=none]
\addplot[
draw = blue, smooth, ultra thick,
domain=0:4,
] {sqrt(x)}
foreach \x in {1,2,3,4} { (axis cs:{\x},0) node[below left] {\x} };
\end{axis}
\end{tikzpicture}

1. how do I shade between the curve and x-axis on [0,4]
2. I don't need the arrows on the axis
3 where does \end{axis} actually end?
4. suggestions...

looked at various samples but there was a lot of versions
going to post this with a problem on LinkedIn so trying to make it look the best
however don't think they render tikz and probably not script ,,,, maybe
its all new to me
thanks ahead...

 

[I like Serena]

1. how do I shade between the curve and x-axis on [0,4]
2. I don't need the arrows on the axis
3 where does \end{axis} actually end?
4. suggestions...

1. We can add \addplot[fill=cyan!30, draw=none, domain=0:4] {sqrt(x)} \closedcycle; to shade the curve up to $x=4$.
2. If we specify axis lines*=middle with a star (*) then the arrows are omitted.
3. The axis ends at $x=5$ because that was specified with xmax=5.
4. We can use xtick={1,2,3,4}, ytick=\empty instead of ticks=none and a foreach to draw ticks.

\begin{tikzpicture}[scale=1]
%preamble \usepackage{pgfplots}
\begin{axis}[xmin=-1, xmax=5, ymin=-1, ymax=3, axis lines*=middle, xtick={1,2,3,4}, ytick=\empty]
\addplot[fill=cyan!30, draw=none, domain=0:4] {sqrt(x)} \closedcycle;
\addplot[
draw = blue, smooth, ultra thick,
domain=0:4,
] {sqrt(x)};
\end{axis}
\end{tikzpicture}