Upper approximating rectangles with tikz?

Question

For lower approximating rectangles, using this answer I was able to draw as many rectangles as I want

\documentclass{standalone} 
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{pgfplots} 
\pgfplotsset{compat=newest} 
%Added
\tikzset{
point/.style={circle,draw=black,inner sep=0pt,minimum size=3pt}
}
\pgfplotsset{
    soldot/.style={color=blue,only marks,mark=*}
    }

\begin{document}
\begin{tikzpicture}
\begin{axis}[
    xtick={4},ytick={0},
    xticklabel={$1$},
    xlabel=$x$,ylabel=$y$,
    y=0.3cm, xmax=4.4,ymax=17.8,ymin=-2,xmin=-0.5,
    enlargelimits=true,
    axis lines=middle,
    clip=false,
    domain=0:4,
    axis on top
    ]
\addplot [fill=blue!30, ybar interval, samples=52]
    {x^2}\closedcycle;
\addplot[smooth,blue, thick,domain=0:4]{x^2};
%\addplot[soldot,red]coordinates {(4,16)} node [anchor=west,text=black]  {$(1,1)$};
\addplot[const plot] coordinates {(4,0)(4,16)};
\end{axis}
\end{tikzpicture}
\end{document}

Output(For 50 rectangles):

How can draw the upper approximating rectangles for any number of rectangles(Take 50 rectangles for instance).

Note: Your blue rectangles are not really below the curve. They are because your curve is strictly increasing. — Paul Gaborit, Mar 21 '18 at 07:30

score 6 · Accepted Answer · answered Mar 21 '18 at 08:00

For the parabola function in your case this is pretty easy by just shifting it to the left according to the bar width. Have a look at the comments in the code on how to do this.

\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
        % define some parameters which are later used
        % for the functions
        \pgfmathsetmacro{\DomainMin}{0}
        \pgfmathsetmacro{\DomainMax}{4}
        \pgfmathtruncatemacro{\Samples}{25}
        % calculate the width of the resulting bars
        \pgfmathsetmacro{\BarWidth}{(\DomainMax-\DomainMin)/\Samples}
    \begin{axis}[
        xmin=-0.5,
        xmax=4.4,
        ymax=17.8,
        ymin=-2,
        axis lines=middle,
        domain=\DomainMin:\DomainMax,
        samples=\Samples,
        axis on top,
    ]
        % use the calculated bar shift value to shift the function
        \addplot [fill=red!30,ybar interval]  {(x+\BarWidth)^2};
        \addplot [fill=blue!30,ybar interval] {x^2};
        \addplot [smooth,blue,thick]{x^2};
    \end{axis}
\end{tikzpicture}
\end{document}

Yes, but could you get rid of the lower rectangles in blue? – Maryà Mar 21 '18 at 08:35 — Maryà, Mar 21 '18 at 08:35
comment the second \addplot line!? – Stefan Pinnow Mar 21 '18 at 08:38 — Stefan Pinnow, Mar 21 '18 at 08:38

Upper approximating rectangles with tikz?

1 Answers1