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I'm new to TikZ and pgfplots but would like to know how to plot the square as well as how to plot the arrows + delta x as well as arrow + delta A:

enter image description here

I'd be most grateful if some of you had some examples I could learn from.

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Welcome to TeX.sx! I included your image as an picture rather than a link. Soon, you will have enough reputation to do it yourself. – Qrrbrbirlbel Oct 8 '12 at 14:58
Related? tex.stackexchange.com/questions/30763/… – Dror Oct 8 '12 at 15:05
@Qrrbrbirlbel: Thanks. Dror: It's a little useful, but I don't think it answers all my questions. – johankj Oct 8 '12 at 15:13
also related (?) tex.stackexchange.com/questions/40780/… – cmhughes Oct 8 '12 at 15:14
@cmhughes: Looks like I have the "square" part of my question answered. Thanks for the links. – johankj Oct 8 '12 at 15:18
up vote 18 down vote accepted

To answer the specific questions, using TikZ:

  1. To draw curved paths, you can use various methods, described in Section 51.3 Curves of the pgfmanual. Some examples using in=,out=, bend and controls=:

    \node at (2,2) (a) {A};
    \node at (0,0) (b) {B};
    \draw[red,->] (a) to[out=0,in=90] (b);
    \draw[green,->] (a) to[out=180,in=90] (b);
    \draw[blue,->] (a) to[out=-90,in=0] (b);
    \node at (4,2) (c) {C};
    \node at (2,0) (d) {D};
    \draw[olive,->] (c) to[bend right] (d);
    \draw[cyan,->] (c) to[bend left=90] (d);
    \node at (7,2) (e) {E};
    \node at (5,0) (f) {F};
    \draw[magenta,->] (e) to[controls=+(90:1) and +(180:1)]  (f);

enter image description here

  1. The dashed rectangle and the arrows for \delta x can be obtained in a number of ways; for example,

    \draw[dashed] (0,0) rectangle (2,3); 
    \node at (4,1.5) (delta) {$\delta x$};
    \draw[<-] (delta) -- +(-30pt,0);
    \draw[<-] (delta) -- +(30pt,0);

enter image description here

An here's one possibility for drawing the complete diagram, using the intersections library:



\begin{tikzpicture}[scale=0.7,transform shape]

% a macro for the axes, the curve and the two vertical lines
\draw[->] (-0.3,0) -- (5,0) node[right] {$x$} coordinate (x axis);
\draw[->] (0,-0.3) -- (0,3) node[above] {$y$};
\draw [name path=curve] (0.5,2) .. controls (1.5,2.8) and (3.5,1) .. (4.5,2);
\path [name path=line 1] (1,0) -- (1,3);
\path [name path=line 2] (4,0) -- (4,3);
\path [name intersections={of=curve and line 1, by={a}}];
\path [name intersections={of=curve and line 2, by={b}}];
\draw (1,0) node[below] {$a$} -- (a);
\draw (4,0) node[below] {$b$} -- (b);

% the initial drawing
\node[above=10pt] at (b) {$y=f(x)$};

% the middle drawing
\path [name path=line 3] (2.5,0) -- (2.5,3);
\path [name path=line 4] (2.8,0) -- (2.8,3);
\path [name path=line 5] (2.2,0) -- (2.2,3);
\fill [name intersections={of=curve and line 3, by={c}}] (c) circle (2pt) node[above right] {$P(x,y)$};
\path [name intersections={of=curve and line 4, by={d}}];
\path [name intersections={of=curve and line 5, by={e}}];
\draw[dashed] (2.5,0) -- (c);
\draw[dashed] (2.8,0) -- (d);
\draw[<->,shorten >=2pt,shorten <= 2pt] (2.2,0) -- node[left] {$y=f(x)$} (e);
\node at (2.65,-0.3) (delta) {$\delta x$};
\draw[<-] (delta) -- +(-20pt,0);
\draw[<-] (delta) -- +(20pt,0);

% the rightmost drawing
\draw[dashed] (0,0) rectangle (0.3,2); 
\node at (0.15,-0.3) (delta) {$\delta x$};
\draw[<-] (delta) -- +(-20pt,0);
\draw[<-] (delta) -- +(20pt,0);
\draw[<->,shorten >=2pt,shorten <= 2pt] (-0.3,0) -- node[left] {$y=f(x)$} (-0.3,2);
\node at (1,2.3) (deltaA) {$\delta A$};
\draw[->] (deltaA) to[out=180,in=90] (0.15,1.8);


enter image description here

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Very nice drawing! Can this also be done using PSTricks? (Well, of course it can, but how?) I would maybe like to use this in notes for my students later this year or next year, and I only use PSTricks for drawings. – Svend Tveskæg Nov 4 '12 at 17:46
@SvendMortensen surely it can be done with PS-Tricks, but I don't use it, so I cannot provide the code. Your question won't be seen by many people here, so perhaps it would be best to repost it as a fresh question? Follow-up questions like this are more than welcome! You can link to this question to provide the background. – Gonzalo Medina Nov 4 '12 at 19:51
@Gonzalo Medina: How about the area under the curve x = f (y)? (with TikZ) – kalakay Nov 22 '13 at 9:37

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