Subscript, Superscript, and Bracket

Question

I want to write like this:

But when I write

\documentclass{article} \usepackage{mathtools} \begin{document} \begin{equation} \lim\limits_{\Delta\rightarrow0}\Delta{}_{t=0}^{t=T}\left\vert\dfrac{df(t)}{dt}\right\vert^2 dt \end{equation} \end{document}

The output was like this

Anyone can tell me what is my mistake?

Answer 1

The _{t=0}^{t=T} in your line makes these things the superscript and subscript of the \lim\limits_{\Delta\rightarrow0}{}. I would do it using \prescript from mathtools package.

\usepackage{mathtools}

and then in the math environment:

\lim\limits_{\Delta\rightarrow0}{} \Delta\prescript{t=T}{t=0}{\left\vert\dfrac{df(t)}{dt}\right\vert^2 dt}

This provides the result as follows:

Answer 2

Here's an attempt to faithfully reproduce the first screenshot you posted.

\documentclass{article}
\usepackage{array}
\usepackage{newtxtext,newtxmath} % optional
\begin{document}
\[
\lim_{\Delta\phantom{\to}0} \Delta
\begin{array}{>{\scriptstyle}l@{}} t=T \\ t=0 \end{array}
\Bigl| \frac{df\!(t)}{dt} \Bigr|^2 dt
\]
\end{document}

Answer 3

Using...tensor package.....with the enviroment mathtools...an alternative a bit more complicated :-)

\documentclass[12pt]{article}
\usepackage{mathtools}
\usepackage{tensor}

\begin{document}
\[\lim_{\Delta\phantom{\to}0} \Delta \tensor*[^T_t]{\bigg\lvert \frac{df(t)}{dt}\bigg\rvert}{^2} dt\]
\end{document}  

Update 1

Using \lower-0.01em with \hbox and \scriptstyle it is possible a nice alignment between T and 2.

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools}
\usepackage{tensor}

\begin{document}
\[\lim_{\Delta\to 0} \Delta \tensor*[^{\lower-0.01em \hbox{$\scriptstyle T$}}_t]{\bigg\lvert \frac{df(t)}{dt}\bigg\rvert}{^2} dt\]
\end{document}