Horizontal Paraboloic Cylinder

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\documentclass{article}
%
% File name: horizontal-paraboloic-cylinder.tex
% Description: 
% The graph of the surface
% z = 4 - x^{2} 
% for -2 <= x <= 2, and 0 <= y <= 4 is generated. 
% Also, the region -2 <= x <= 2, and 0 <= y <= 4 
% is shown.
% 
% Date of creation: April, 23rd, 2022.
% Date of last modification: April, 23rd, 2022.
% Author: Efraín Soto Apolinar.
% https://www.aprendematematicas.org.mx/author/efrain-soto-apolinar/instructing-courses/
% Terms of use:
% According to TikZ.net
% https://creativecommons.org/licenses/by-nc-sa/4.0/
% 
\usepackage{tikz}
\usetikzlibrary{patterns}
\usepackage{tikz-3dplot}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{1pt}
%
\begin{document}
    %
    \tdplotsetmaincoords{60}{110}
    \begin{tikzpicture}[tdplot_main_coords,scale=0.85]
        \pgfmathsetmacro{\step}{0.01}
        %%% Coordinate axis
        \draw[thick,->] (0,0,0) -- (2.5,0,0) node [below left] {\footnotesize$x$};
        \draw[dashed] (0,0,0) -- (-2.5,0,0);
        \draw[thick,->] (0,0,0) -- (0,4.5,0) node [right] {\footnotesize$y$};
        \draw[dashed] (0,0,0) -- (0,-0.5,0);
        \draw[thick] (0,0,0.0) -- (0,0,4.0);
        % Region of integration
        \draw[gray,thick,fill=yellow,opacity=0.35] (2,0,0) -- (2,4,0) -- (-2,4,0) -- (-2,0,0) -- cycle;
        \draw[blue,thick,opacity=0.5] (2,0,0) -- (2,4,0) -- (-2,4,0) -- (-2,0,0) -- cycle;
        % The curves slicing the surface
        \draw[blue,thick,opacity=0.5] plot[domain=-2:2,smooth,variable=\t] ({\t},{0},{4.0 - \t*\t}); 
 
 
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