# Writing limits of integration [duplicate]

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.

• This could help with adjustments: tex.stackexchange.com/a/46968/14757 To insert limits, use _0^9 May 1 '15 at 14:51
• Try $\left. abc \right|^9_1$ May 1 '15 at 14:52
• I would define a command \DeclarePairedDelimiter\eval.\rbrack and use \eval{..}_{1}^{9}. May 1 '15 at 14:54
• Typesetting aside, I would not use this vertical line notation if the expression in front of it involves additive terms. Better choose square brackets, and decorate the closing ] with the limits _1^9. For instance you might have [2+x]_1^9=8. In your notation, this might be misread as 2+[x]_1^9=10. May 1 '15 at 15:17

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).

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.

• ] is not used to indicate the evaluation of an integral. May 1 '15 at 19:34
• @user69453: I don't think so, as I've seen it used for this purpose several times before. The text of this question is an example, that indeed didn't surprise me. If you like, \right| should make it, also. May 1 '15 at 19:44
• The impression I got from 'I would like to draw the line after an integral has been "solved,"' was that the original poster desired a vertical line, but had been unable to produce one for their example, and so had substituted a ]. That's why I answered the question the way I did. However, this answer is a very good answer to the question as posed and a perfectly plausible interpretation of it. May 1 '15 at 23:40
• @user69453: I've edited my answer, even if I focused more on \right vs. \Bigr, rather than ] vs. |. Have a check ;) May 2 '15 at 9:58
• I'll remove my downvote :) May 2 '15 at 10:57