PGFPlots - Using "smooth" doesnt render smooth curves, but "samples" doesnt work either

I’m using PGFPlots to generate graphs of functions. I use smooth to smooth out the curve, but it isn’t smooth enough. So I tried increasing the samples option. The problem is, I can go all the way to samples=9000 yet the graph won’t draw until the end. Here are some pictures:

Using just smooth:

Using smooth and samples=10:

Using smooth and samples=950:

Using smooth and samples=2950:

As can be seen, using just smooth yields a lumpy picture, whereas using high samples along with smooth gives a great curve, but doesn’t go up to the x-axis, as it should, and using highersamples values seems to give diminishing returns.

Code:

documentclass[margin=5mmm, tikz]{standalone}
usepackage{pgfplots}
usepackage{tikz}
usepgfplotslibrary{fillbetween}
pgfplotsset{compat=1.8}

begin{document}
    begin{tikzpicture}[xscale = 1.7]
        begin{axis}
        [
            xmin=0,xmax=4,
            ymin=0,ymax=12,
            axis x line=middle,
            axis y line=middle,
            axis line style=->,
            ticks=none,
        ]
        % The line below is the important one
        addplot[name path = c, color=blue, domain=0:4, samples=950, smooth]{x^2 * (9 - x^2)^0.5};
        addplot[name path = a, domain=0:4]{0};
        addplot [
            thick,
            color=blue,
            fill=blue,
            fill opacity=0.05
        ]
        fill between[
            of=a and c,
        ];
        end{axis}
    end{tikzpicture}
end{document}

I’m adding the code to highlight under the graph where you can see how the colored area acts weird because it might be useful to you to see the strange behavior of the curve when samples are used.

Is there any way to fix this, i.e. get a smooth curve without this happening?