Writing limits of integration

Question

I'm not sure exactly what it's called, but I would like to draw the line after an integral has been "solved," showing limits of integration, like so:

There is a line with a 9 above and 1 below.

Answer 1

Assuming that what you are looking for is:

You can do this quite nicely with \Biggr|:

\[
  2x + \frac{2}{3}x^{\frac{3}{2}} + \frac{1}{x}\Biggr|_{1}^{9}
\]

Personally, I prefer this approach. As you can see the line extends slightly above and below the the expression to its left. It also saves you having to have a preceding \left.

Use \Biggr| where you have a "tall" expression (e.g. with fractions, like here) and you can just use \Bigr| for "short" ones, e.g.:

\[
  y \cdot x(y)\Bigr|_{y_{1}}^{y_{2}}
\]

Produces:

You can also use \Bigl| for a lone vertical line to the left, or you can pair them if ever you wish to do so.

This \Bigl and \Bigr format can be used with other types of bracket, too, e.g. \Bigr]

As Benjamin McKay points out in the comments, you could also use:

\[
  \left. 2x + \frac{2}{3}x^{\frac{3}{2}} + \frac{1}{x}\right|_{1}^{9}
\]

This is an excellent solution if you want your vertical line to be the same height as the preceding expression. Generally \left( and \right) should scale the brackets so that they are the same height as what they enclose. With \Bigl( & \Bigr) and \Biggl( & \Biggr) you are using brackets of a fixed height. A \right must always be paired with a \left, while \Bigr| does not have this problem. This is why you must use \left. and \right|. If you don't want a left hand bracket, you must have \left. (and vice versa if you don't want a right hand bracket).

Answer 2

This solution:

\documentclass{article}

\begin{document}

\[
\int^b_a f(x)dx=\left. F(x) \right]^b_a=F(b)-F(a)
\]

\[
\int^b_a f(x)dx=\left. \frac{F(x)}{1} \right]^b_a=F(b)-F(a)
\]

\[
\int^b_a f(x)dx=\left. \frac{\frac{F(x)}{1}}{270-269} \right]^b_a=F(b)-F(a)
\]

\end{document}

adjusts properly, as the height and width of the content between \left. and \right]^b_a change. The output:

Addendum: At the same way, if one replaces the three occurrences of \right]^b_a with \right|^b_a in the code above, the same delimiter satisfies again each of the three cases:

---

In my opinion, \Bigr| (compared to \right|) has the "advantage" that it doesn't need any \left. before, but it also has two minor "disadvantages".

1) It requires \usepackage{amsmath} in the preamble (but this is not the problem, since anybody writing a paper with such contents would use this package anyway, I guess).

2) One must be chosen case by case among \bigr|, \Bigr|, \biggr|, \Biggr| (see 4.14.1 at page 15) and this choice is not always enough: the code

\documentclass{article}

\usepackage{amsmath}

\begin{document}

\[
\int^b_a f(x)dx=
\frac{F(x)}{\frac{\binom{n}{n}}{\binom{k}{k}}} \Biggr|^b_a=
F(b)-F(a)
\]

\end{document}

produces

On the other hand, in case of such height or more, the use of \left./\right| instead is not trivial too (for my level of experience) and should be further tested.