Here's some TikZ I got off the TikZ site and beginner-hacked. It should be just an x-y graph with a Bezier curve for a function f(x), then points x1 and x2. I want a shaded rectangle x1 -- f(x1) -- f(x2) -- x2 to represent the area under the curve between x1 and x2 (but flat-topped) instead of the shaded triangle above the desired rectangle. The second dot on the Bezier needs to go away too. Specifically, I don't understand what \coordinate (O) at (0,0); nor what \scope[name intersections = {of = x and y, name = i}] \fill[gray!20] (i-1) -- (i-2 |- i-1) -- (i-2) -- cycle; is doing. What's going on with the i variable(?)? Any ideas for a good tutorial on these matters would be appreciated.

\begin{document}
\begin{tikzpicture}[
scale=2,
thick,
>=stealth',
dot/.style =
{draw, ho fill = white, circle, inner sep = 0pt, minimum size = 4pt}
]
\coordinate (O) at (0,0);
\draw[->] (-0.3,0) -- (7,0) coordinate[label = {below:$x$}] (xmax);7
\draw[->] (0,-0.3) -- (0,5.5) coordinate[label = {right:$y$}] (ymax);
\path[name path=x] (0.3,0.5) -- (6.7,4.7);
\path[name path=y] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
\scope[name intersections = {of = x and y, name = i}]
\fill[gray!20] (i-1) -- (i-2 |- i-1) -- (i-2) -- cycle;
\draw[red] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.8) (6,5)};
\draw (i-1) node[dot, label = {above:$f(x_1)$}] (i-1) {} -- (i-1 |- O) node[dot, label = {below:$x_1$}] {};
\path (i-2) node[dot] (i-2) {} -- (i-2 |- i-1) node[dot] (i-12) {};
\draw           (i-12) -- (i-12 |- O) node[dot,
label = {below:$x_2$}] {};
\draw (i-1) --  (i-12);
\path       (i-1 |- O) -- (i-2 |- O);
\endscope
\end{tikzpicture}
\end{document}

• Please extend your code to complete document. Also it has error in definition of dot (correct is fill not ho fill). – Zarko Jan 1 '17 at 4:21
• Please attribute others' code fairly. At least say who and provide a link. How am I supposed to find the original from that description? – cfr Jan 1 '17 at 4:26
• (i-1) and (i-2) are the intersections of the paths named x and y. Initially. Then they become the names of nodes later on, along with (i-12). See the manual coverage of the intersections library for further information. There are other errors beside the one @Zarko mentioned. What is that stray 7 doing, for example? – cfr Jan 1 '17 at 4:34

Edit: My first two assumptions was wrong :(, your problem is more simple ... so I replace the first solution with correct one :) and in addendum left the second one. Next time, please provide complete document beginning with \documentclass{...} and necessary packages/libraries in preamble (see MWE below). After eliminating error in definition of dot and removing all unnecessary code, the MWE, which generate showed image is:

\documentclass[tikz, margin=3mm]{standalone}
\usetikzlibrary{arrows, backgrounds, intersections, positioning}

\begin{document}
\begin{tikzpicture}[%scale=2,
node distance = 0pt,
> = stealth',
font = \footnotesize,
dot/.style = {draw, fill = white, circle, inner sep = 0pt, minimum size = 4pt}
]
\coordinate (O);
% axis
\draw[->] (-0.3,0) -- (7,0.0) node[below left] {$x$};
\draw[->] (0,-0.3) -- (0,5.5) node[below left] {$y$};
% curve
\draw[red, name path=y] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.7) (6,5)};
% intersection at x_1 and x_2
\path[name path=x] (0.3,0.5) -- (6.7,4.7);
\draw[name intersections={of=x and y, by={f1,f2}},fill=white]
(f1) circle (2pt) node[above] {$f(x_1)$}
(f2) circle (2pt) node[above left] {$f(x_2)$};
% gray area
\begin{scope}[on background layer]
\draw[fill=gray!20,very thin] (f1) rectangle (f2 |- O);
% x-coordinates
\node[below=of f1 |- O] {$x_1$};
\node[below=of f2 |- O] {$x_2$};
% x-coordinates
\node[below=of f1 |- O] {$x_1$};
\draw[dashed,very thin]  (f2) -- (f2 |- f1); % <-- delete if it is surplus
\end{scope}
\end{tikzpicture}
\end{document}


The MWE is structured so it should be easy to determine functions of each code parts. In code is used:

• coordinate O for determining position for $x_1$ and $x_2$ by (f1 |- O) and (f2 |- O) respectively (I rename intersection names to f1 and f2)
• by intersections library are calculated intersection of line with name x and curve with name y (read cfr comment above, why you not drawn it?)
• coordinates of intersections are used for placings labels of intersection as well of labels of x-coordinates on x-axis

I slightly redesign your images (use of dashed lines). Library backgrounds is used that grayed area is on layer behind of the curve,positioning for placement of nodes with labels $x_1$ and $x_2$. then the code is slightly more sophisticated. First we draw curve as closed path and than with \clip chop out the part between $x_1$ and $x_2$.

\documentclass[tikz, margin=3mm]{standalone}
\usetikzlibrary{arrows, backgrounds, intersections}

\begin{document}
\begin{tikzpicture}[%scale=2,
> = stealth',
font = \footnotesize,
dot/.style = {draw, fill = white, circle, inner sep = 0pt, minimum size = 4pt}
]
\coordinate (O);
% axis
\draw[->] (-0.3,0) -- (7,0.0) node[below left] {$x$};
\draw[->] (0,-0.3) -- (0,5.5) node[below left] {$y$};
% curve
\draw[red, name path=y] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.7) (6,5)};
% intersection at x_1 and x_2
\path[name path=x] (0.3,0.5) -- (6.7,4.7);
\draw[name intersections={of=x and y, by={f1,f2}},fill=white]
(f1) circle (2pt) node[above] {$f(x_1)$}
(f2) circle (2pt) node[above left] {$f(x_2)$};
% gray area
\begin{scope}[on background layer]
\clip   (f1 |- O) rectangle (f2);
\fill[gray!20] plot[smooth] coordinates {(-0.3,2) (2,1.5) (4,2.7) (6,5)}
|- (O) -| (-0.3,2);
\end{scope}
\draw[dashed,very thin] (f1 |- O) node[below] {$x_1$} -- (f1)
(f2 |- O) node[below] {$x_2$} -- (f2);
\end{tikzpicture}
\end{document}

• Thanks much for the good tips. However, I'd like the shaded part to be a rectangle with sides $x_1 - f(x_1)$ by $f(x_1) - f(x_2)$, i.e., the rectangle under the curve. (Also, how does one do MathJax/Latex on this forum?) I would show you the original image I'm trying to get, but it got taken down. . . . – 147pm Jan 1 '17 at 16:15
• sorry, I do not understand where. can you edit your question and add hand drawn sketch, what you like to be shaded? – Zarko Jan 1 '17 at 17:02
• Check out borgauf.macsyma.org/p0.pdf "Figure 1" – 147pm Jan 1 '17 at 18:31
• oh, so simple ... :) see edited answer. – Zarko Jan 1 '17 at 18:59