Paraboloid

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\documentclass{article}
%
% File name: classic-paraboloid.tex
% Description: 
% The graph of the surface
% z = x^{2} + y^{2}
% is generated. Also, the region x^2 + y^2 \leq 1
% 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=2.0]
        \pgfmathsetmacro{\tini}{0.5*pi}
        \pgfmathsetmacro{\tfin}{1.85*pi}
        \pgfmathsetmacro{\tend}{2.5*pi}
        % Node indicating the equation of the circumference
        \draw[white] (1.35,0,0) -- (0,1.35,0) node [red,below,midway,sloped] {$x^2 + y^2 = 1$};
        %%% Coordinate axis
        \draw[thick,->] (0,0,0) -- (1.5,0,0) node [below left] {\footnotesize$x$};
        \draw[dashed] (0,0,0) -- (-1.25,0,0);
        \draw[thick,->] (0,0,0) -- (0,1.5,0) node [right] {\footnotesize$y$};
        \draw[dashed] (0,0,0) -- (0,-1.25,0);
        % The region of integration
        \fill[yellow,opacity=0.35] plot[domain=0:6.2832,smooth,variable=\t] ({cos(\t r)},{sin(\t r)},{0.0});
        \draw[red,thick] plot[domain=0:6.2832,smooth,variable=\t] ({cos(\t r)},{sin(\t r)},{0.0});
 
 
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