Area under arbitrary curve tikz

Question

I'm using tikz to create two arbitrary curves and fill the area between them. What I'm trying to do is:

This is my approach:

\documentclass{standalone}
\usepackage{amsmath}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[line join=round]
\draw [-latex,thick] (-0.5,0)  -- (4.5,0) node[below]{$x$};
\draw [-latex,thick] (0,-0.5)  -- (0,3.5) node[left]{$y$};
\draw [fill=white!50!blue,opacity=0.3, smooth,samples=100,domain=0.5:3.5] plot(\x, {sin(\x200)0.25+0.5}) -- plot(\x, {sin(\x200)0.25+2.5}) -- cycle;
\draw (0,0) node[below left]{$0$} ;
\draw (2,1.5) node[]{$D$} ;
\draw [blue, domain=-0.25:4, smooth, variable=\x] plot (\x, {sin(\x200)0.25+0.5});
\draw [blue, domain=-0.25:4, smooth, variable=\x] plot (\x, {sin(\x200)0.25+2.5});
\draw [blue] (0.5,-0.25) -- (0.5,3) ;
\draw [blue] (3.5,-0.25) -- (3.5,3);
\draw (0.5,0) node[below left]{$a$} ;
\draw (3.5,0) node[below right]{$b$};
\draw (4,3) node[right]{$y=\psi(x)$} ;
\draw (4,1) node[right]{$y=\varphi(x)$};
\end{tikzpicture}
\end{document}

And what I get:

I don't know how to fix these crossed lines.

I'm also having trouble to define the sin(\x*200)*0.25+2.5 in the y axis, to get something very similar:

Probably gnuplot - Fill the area between two curves calculated by pgfplots - TeX - LaTeX Stack Exchange / tikz pgf - filling area between 2 functions, with shading - TeX - LaTeX Stack Exchange but this is GNUplot? — user202729, Jan 07 '22 at 04:27

score 9 · Accepted Answer · answered Jan 07 '22 at 05:20

9

\documentclass[tikz, border=1cm]{standalone}
\begin{document}
\begin{tikzpicture}
\draw [fill=white!50!blue, opacity=0.3, smooth, samples=100, domain=0.5:3.5] plot(\x, {sin(\x*200)*0.25+0.5}) -- plot[domain=3.5:0.5] (\x, {sin(\x*200)*0.25+2.5}) -- cycle; 
\draw[yshift=-3cm, fill=white!50!red, opacity=0.3, smooth, samples=100, domain=0.5:3.5] plot({sin(\x*200)*0.25+0.5},\x) -- plot[domain=3.5:0.5] ({sin(\x*200)*0.25+2.5},\x) -- cycle; 
\end{tikzpicture}
\end{document}

answered Jan 07 '22 at 05:20

hpekristiansen

37,006

Thank you so much. – Mario Tafur Jan 07 '22 at 05:28
1

(summary. Add [domain=3.5:0.5] to the second plot so that it traces the outline in backwards direction.) – user202729 Jan 07 '22 at 12:28

Don Hosek · Answer 2 · 2022-01-07T18:39:49.987

As usual when something strange comes out of a computer, it's because it's doing exactly what you told it to do.

The problem is this line:

\draw [fill=white!50!blue,opacity=0.3, smooth,samples=100,domain=0.5:3.5] plot(\x, {sin(\x*200)*0.25+0.5}) -- plot(\x, {sin(\x*200)*0.25+2.5}) -- cycle;

You've told it to fill a region starting from 0.5 to 3.5 following the function sin(200x)+0.5 then connect that to a plot from 0.5 to 3.5 following the function sin(200x)+2.5 and then join to the starting point. So your region enclosure goes from the bottom right to the top left and then from the top right back to the bottom left.

How to fix this? Well you need to tell LaTeX to graph one of those functions from right to left instead of left to right. Time to brush off those dusty high school algebra skills. We replace all the instances of \x in one function to 4-\x (since the domain is 0.5–3.5). Replacing the problematic line with:

\draw [fill=white!50!blue,opacity=0.3, smooth,samples=100,domain=0.5:3.5] plot(\x, {sin(\x*200)*0.25+0.5}) -- plot(4-\x, {sin((4-\x)*200)*0.25+2.5}) -- cycle;

will give the desired results.

For your second graph, you're essentially doing an inverse function graph which means swapping x and y. In TikZ terms this means swapping the first and second parameters in coordinates and plot statements.

Area under arbitrary curve tikz

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