I was having some thought about what would be the syntax to make the end point evaluation of derivatives or integrals. Such as making the | with the two end points of evaluation on the top an bottom of the line. Any suggestions would be wonderful.
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11I was really hoping this was going to be a question about doing symbolic integration and differentiation in TeX. Alas, it was actually about typesetting. =)– TH.Commented Apr 15, 2011 at 17:07
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3I came here interested in typesetting, and found it useful.– Ross MillikanCommented Jun 15, 2011 at 5:07
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6 Answers
The \big| or \Big| symbols work quite well
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[ \int_a^b x^2\;\mathrm{d}x= \tfrac{1}{3} x^3 \Big|_a^b \]
\end{document}
answered Apr 15, 2011 at 15:05
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1Thank You Danie, that worked excellent. Just what I was looking for. One question while on the topic. I noticed you using
\tfrac, is there any significance to that over using\dfrac. How different are they and what do they actually mean if you know? Meaning the 't' and 'd'. Commented Apr 15, 2011 at 15:13 -
4@night owl:
\tfracis the inline "text" mode fraction and\dfracthe display math frac.\tfracis smaller and I prefer it for single line equations. Commented Apr 15, 2011 at 15:35 -
Thank You. That was very useful to know for later references. Commented Apr 15, 2011 at 15:56
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2@night:
\tfracis nice for numerical fractions but I would avoid it when variables are in the numerator or denominator. Commented Apr 15, 2011 at 18:48 -
How do you get that integral sign like that. Mines looks loose and sloppy at the ends. Using: $ \displaystyle\int f(x)\ dx. $ OR $$ \displaystyle\int f(x)\ dx. $$ Commented Apr 19, 2011 at 11:54
The \left - \right construct gives you an expandable evaluation symbol:
\documentclass[12pt]{article}
\usepackage{amsmath}
\DeclareMathOperator{\di}{d\!}
\newcommand*\Eval[3]{\left.#1\right\rvert_{#2}^{#3}}
\begin{document}
\[
\int_{a}^{b}x\di x = \Eval{\dfrac{1}{2}x^{2}}{a}{b}
\]
\[
\int_{a}^{b}\di x = \Eval{x}{a}{b}
\]
\end{document}
EDIT: I modified the code following the comment by Ryan Reich.
answered Apr 15, 2011 at 15:19
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Thanks for the response. Your looks clean, just a tad bit more work. hehe.. +1 Commented Apr 15, 2011 at 15:57
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9You could just write
\left.\frac{1}{2} x^2\right|_a^b, too. Commented Apr 15, 2011 at 18:13 -
6+1 I prefer this over using the
\big|or\Big|symbols because of the expandability - you may have a very complex expression of which you don't know the vertical extent, and hence which size modifier for the|. It's a "tad bit more work" up front as @night owl pointed out, but you don't need to tweak and recompile to get it looking just right :).– cm2Commented Sep 27, 2011 at 15:32 -
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2@anton it's a placeholder because there has to be an argument there, but we don't actually want anything printed. It is a special case specifically designed for this purpose; no period is actually shown. Commented May 8, 2022 at 19:28
If you want the evaluation symbol to be of the same height as the integration symbol, you can enclose a phantom integration symbol between \left and \right, like this:
\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator*{\di}{\mathrm{d}\!}
\def\at{
\left.
\vphantom{\int}
\right|
}
\begin{document}
\begin{eqnarray}
\int_a^b x^2 \di x &=& \frac{x^3}{3}\at_a^b \\
\int\limits_a^b x^2 \di x &=& \frac{x^3}{3}\at_a^b
\end{eqnarray}
\end{document}
The commath package has the \eval command for this purpose.
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3
This hasn't got anything to do with your question, but I'll post it anyway (it's on topic I guess).
I don't know if this is correct (since few people do it), but I like it when the integration limits are above and below the integral sign:
\DeclareMathOperator{\di}{d\!}
\[
\int\limits_a^b\! x\di x = \tfrac{1}{2}x^2\Big|_a^b
\]
As you can see, adding the macro \limits to your code makes the integral look good. You can do this for any math operator.
Also notice that the \! command brings the integrandum closer to the integral sign. I like this kind of snugged integrals.
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.. unusual, is there a maths book or article using it? I would be interested in having a look.– yannislCommented Apr 16, 2011 at 17:22
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@Yiannis: As I said, don't know if it's the correct way of typesetting integral bounds, I just like it myself. I geuss I've seen it around somewhere, just can't remember where.– romeovsCommented Apr 16, 2011 at 18:15
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4This is the standard way of typesetting integration limits in Russian literature. Commented Aug 16, 2016 at 21:26
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This is probably not done because the integral symbol's already pretty tall, so stacking over- and underscripts on it fills even more vertical space.– ChappersCommented May 27, 2017 at 21:48
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@chappers, would it make sense to align the integration bounds of the integral (lhs) with those of the evaluation (rhs)? since the vertical space is already used up... maybe that's the Russian logic... I just noticed that denshion's answer below addresses this possibility.– PatrickTCommented Oct 8, 2022 at 20:59
None of the stuff here gave me the desired outcome in the editor I was using (MATLAB live script), but I found this and it's really nice:
\bigg/_{\!\!\! a}^{\,b}
Example:
\frac{\sqrt{\pi}}{2}\bigg/_{\!\!\! a}^{\,b}x^2
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1I don't know what that means in this context, but maybe someone finds that useful to know.– 0x464eCommented Mar 5, 2021 at 15:46