drawing a dashed area using tikz

Good morning,
I’m trying to reproduce the following pictures to be inserted in my course:

But I don’t have any idea how to obtain the dashed area. Here is my code of the axis:

 documentclass{article}
 usepackage{tikz}

begin{document}

        begin{tikzpicture}[holdot/.style={circle,draw,fill=white,inner sep=1.5pt}]
        draw[help lines, color=gray, dashed] (-4,-3) grid (4,3);
        draw[->,ultra thick] (-4,0)--(4,0) node[right]{$x$};
        draw[->,ultra thick] (0,-3)--(0,3) node[above]{$y$};
        
        draw[thick,red,domain=-1.42:1.42,samples=200] (0.5,2) node[anchor=north west] {$mathcal{C}_{f}$} plot(x,{x^3});
        draw [-, green,thick] (2,0) -- (2,3);
        
        end{tikzpicture}
end{document}

draw[fill=orange] (1,0) -- plot[domain=1:1.2] (x, {x^3}) -- (1.2,0) -- cycle;