# Is there any way to have a "tall bar" with upper and lower limit values, such as used after integrations?

## One formatting thing I'm still curious about and haven't sussed out through examining things on my own is if there's any way to add a "tall bar" to the end of a line, with a superscript and a subscript. I'm envisioning something seen after doing a definite integral, where many authors often put a tall vertical bar at the end of the expression with the limits of integration attached to that bar. Usually that vertical bar extends a bit over the top of the line and a little under the line. The closest I have come up with so far is using the pipe symbol - which does extend about the height I'd want, but as soon as I attach the limits with ^ and _, it immediately shrinks down to regular height, which crams together the limits. For instance: without hashtags int_0^2 x^2 dx = x^3/3 | with hashtags ${\int}_{0}^{2} {x}^{2} \mathrm{dx} = {x}^{3} / 3 |$ without hashtags int_0^2 x^2 dx = x^3/3 |_0^2 with hashtags ${\int}_{0}^{2} {x}^{2} \mathrm{dx} = {x}^{3} / 3 {|}_{0}^{2}$ Any suggestions?

Sep 29, 2017

Yes, but it's (kinda) tedious.

#### Explanation:

An easy way to bypass that problem is to use right brackets instead of a vertical bar.

So, for example, you can write something like this

• without hashtags

int_0^2 x^2 dx = [x^3/3 ]_0^2

• with hashtags

${\int}_{0}^{2} {x}^{2} \mathrm{dx} = {\left[{x}^{3} / 3\right]}_{0}^{2}$

Not ideal, not by a long shot, but you can use it to get the point across. In fact, I think that most contributors use this technique when posting answers on definite integrals.

Now, we do have a way--or possibly more--of adding lower and upper values to a vertical bar, but it takes a bit of creativity and the result is far from perfect.

The idea is that you add the value you want as the lower limit as a fraction with an invisible numerator and an invisible fraction bar.

In your case, you'd have--for illustration purposes, I'll use color(red)() instead of color(white)()

• without hashtags

color(red)(a/color(black)(0))

• with hashtags

$\textcolor{red}{\frac{a}{\textcolor{b l a c k}{0}}}$

Notice that the numerator and the fraction bar are invisible here.

The same principle applies to the value that you want as the upper limit, only this time, you need a fraction with an invisible denominator and an invisible fraction bar.

• without hashtags

color(red)(color(black)(2)/0)

• with hashtags

$\textcolor{red}{\frac{\textcolor{b l a c k}{2}}{0}}$

If you combine the two fractions, you'll get

• without hashtags

int_ 0^2 x^2 dx = x^3/3 |_(color(red)(a/color(black)(0)))^(color(red)(color(black)(2)/a))

• with hashtags

${\int}_{0}^{2} {x}^{2} \mathrm{dx} = {x}^{3} / 3 {|}_{\textcolor{red}{\frac{a}{\textcolor{b l a c k}{0}}}}^{\textcolor{red}{\frac{\textcolor{b l a c k}{2}}{a}}}$

As you can see, the two limits are a little further apart.

Using color(white)() instead of color(red)() for full effect

• without hashtags

int_ 0^2 x^2 dx = x^3/3 |_(color(white)(a/color(black)(0)))^(color(white)(color(black)(2)/a))

• with hashtags

${\int}_{0}^{2} {x}^{2} \mathrm{dx} = {x}^{3} / 3 {|}_{\textcolor{w h i t e}{\frac{a}{\textcolor{b l a c k}{0}}}}^{\textcolor{w h i t e}{\frac{\textcolor{b l a c k}{2}}{a}}}$

As I said, the result is far from perfect--notice that the integration limits were reduced in size because the two fractions must fit the height of the vertical bar--but I'd say that this technique gets the job done :D

If you want, you can experiment with this technique to get the two values even further apart by using more fractions, but that would only make the process more tedious + the results are not going to be that great.

Dec 18, 2017

{:x^3/3|:}_0^2