<< Graphics`FilledPlot`;
L[x_]:= ...
M[x_]:=Piecewise[{{L[x],x<=.2827},{0,x>.2827}}]
FilledPlot[{L[x],M[x]}, {x,0,1}, PlotRange->{0,.0003}, Fills->{Hue[1],GrayLevel[1]}, Ax\ esLabel->[{x,L[x]}]]