using \middle| to include limits during an integration process

Question

i need to include limits (lower and upper ) in the ``\middle|` to solution to an integration.

\begin{eqnarray}
 Area &=& \int_{-1}^{2}(7-x^2)dx \\
&=& \left[\left(7x-\frac{1}{3}x^3\right) \middle| \right] \\ % here is where i wish it to occur
&=& \left[7.2-\frac{1}{3}(8)\right]- \left[7(-1)-\frac{1}{3}(-1)\right] \\
&=& 18 
\end{eqnarray}

To the \middle? I've never seen that syntax before. Here users write it as limits to the ], i.e. ]_1^2. And BTW please don't use eqnarray. — daleif, Oct 10 '13 at 14:20
I've seen [...] and limits attached to the right bracket or ...| and limits attached to the bar; never brackets and bar. — egreg, Oct 10 '13 at 14:22
i am still new at this, so apart from eqnarray what do you recommend? — user38064, Oct 10 '13 at 14:37
instead of eqnarray, look at split or align from amsmath. see eqnarray vs align. — barbara beeton, Oct 10 '13 at 15:02

score 1 · Answer 1 · edited Apr 13 '17 at 12:35

(Summary of comments.)

You can add the limits after the bracket using [...]_{lower}^{upper}. Having both brackets and bar is at best unusual, so stick to one or the other.

Also as mentioned, eqnarray should not be used, environments defined by amsmath is preferred (see eqnarray vs align). Which environment to use depends on what type of numbering you prefer. align gives you a number for each line, aligned (or split) inside an equation gives you a single number for the whole group of equations, and align* gives you no numbers at all.

I also used \text{...} for Area, and I added a thin space (\,) before dx.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
Each step numbered:
\begin{align}
 \text{Area} &= \int_{-1}^{2}(7-x^2)\,dx \\
&= \left[\left(7x-\frac{1}{3}x^3\right) \right]_{-1}^{2} \\ 
&= \left[7\cdot2-\frac{1}{3}(8)\right]- \left[7(-1)-\frac{1}{3}(-1)\right] \\
&= 18 
\end{align}

One number for all:
\begin{equation}
\begin{aligned}
 \text{Area} &= \int_{-1}^{2}(7-x^2)\,dx \\
&= \left[\left(7x-\frac{1}{3}x^3\right) \right]_{-1}^{2} \\ 
&= \left[7\cdot2-\frac{1}{3}(8)\right]- \left[7(-1)-\frac{1}{3}(-1)\right] \\
&= 18 
\end{aligned}
\end{equation}

No numbers:
\begin{align*}
 \text{Area} &= \int_{-1}^{2}(7-x^2)\,dx \\
&= \left[\left(7x-\frac{1}{3}x^3\right) \right]_{-1}^{2} \\ 
&= \left[7\cdot2-\frac{1}{3}(8)\right]- \left[7(-1)-\frac{1}{3}(-1)\right] \\
&= 18 
\end{align*}
\end{document}

using \middle| to include limits during an integration process

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