Height of "parentheses, brackets, braces"

Question

I wonder if there could be a tricky automated way to detect fractions within "parentheses, brackets, braces" to adjust their heights to the maximum height of the candidates. See picture below and highlighted in yellow.

The minimal example is given by:

\documentclass{article}
\usepackage{amsmath,amssymb}
\begin{document}
\begin{align*}
I_x&=\int y^2\,\underbrace{\text{d}A}_{=\text{d}x\text{d}y}=4\left(\int    \limits_{x=0}^{\frac{B}{2}-\frac{b}{2}}\int \limits_{y=0}^{\frac{H}{2}}y^2\,\text{d}y\text{d}x+\int\limits_{x=\frac{B}{2}-\frac{b}{2}}^{\frac{B}{2}}\int \limits_{y=\frac{h}{2}}^{\frac{H}{2}}y^2\,\text{d}y\text{d}x\right)\\
&=4\left(\left[x\right]_{x=0}^{\frac{B}{2}-\frac{b}{2}}\cdot \left[\frac{1}{3}y^3\right]_{y=0}^{\frac{H}{2}}+\left[x\right]_{x= \frac{B}{2}-\frac{b}{2}}^{\frac{B}{2}}\cdot \left[\frac{1}{3}y^3\right]_{y=\frac{h}{2}}^{\frac{H}{2}}\right)\\
&=\frac{BH^3-bh^3}{12}
\end{align*}
\end{document}

Any hints appreciated. As told above - the target is to detect the fractions and then adjust the height to all other parentheses, brackets, braces alike.

The way I did looks quite ugly to my sense of good typing ...

Hope I was precise enough!

Answer 1

I prefer for brackets and parentheses this version. Each of us has a style to write mathematical formulas. The style which suits the most to you would be this.

\documentclass{article}
\usepackage{amsmath,amssymb,mathtools}
\begin{document}
\begin{align*}
I_x&=\int y^2\underbrace{\mathrm{d}A}_{=\mathrm{d}x\mathrm{d}y}=4\left(\int \limits_{x=0}^{\frac{B}{2}-\frac{b}{2}}\int \limits_{y=0}^{\frac{H}{2}}y^2\mathrm{d}y\mathrm{d}x+\int\limits_{x=\frac{B}{2}-\frac{b}{2}}^{\frac{B}{2}}\int \limits_{y=\frac{h}{2}}^{\frac{H}{2}}y^2\mathrm{d}y\mathrm{d}x\right)\\
&=4\left(\bigg[x\bigg]_{x=0}^{\frac{B}{2}-\frac{b}{2}}\cdot \left[\frac{1}{3}y^3\right]_{y=0}^{\frac{H}{2}}+\bigg[x\bigg]_{x= \frac{B}{2}-\frac{b}{2}}^{\frac{B}{2}}\cdot \left[\frac{1}{3}y^3\right]_{y=\frac{h}{2}}^{\frac{H}{2}}\right)\\
&=\frac{BH^3-bh^3}{12}
\end{align*}
\end{document}

Answer 2

\documentclass{article}
\usepackage{amsmath,amssymb}
\let\zzfrac\frac
\def\frac#1#2{\afterassignment\zzztest\count0=0#1#2\relax{#1}{#2}}
\def\zzztest#1\relax{%
\if\relax\detokenize{#1}\relax
  \expandafter\tfrac
\else
  \expandafter\zzfrac
\fi}

\begin{document}
\begin{align*}
I_x&=\int y^2\,\underbrace{\mathrm{d}A}_{=\mathrm{d}x\mathrm{d}y}=4\left(\int    \limits_{x=0}^{\frac{B}{2}-\frac{b}{2}}\int \limits_{y=0}^{\frac{H}{2}}y^2\,\mathrm{d}y\mathrm{d}x+\int\limits_{x=\frac{B}{2}-\frac{b}{2}}^{\frac{B}{2}}\int \limits_{y=\frac{h}{2}}^{\frac{H}{2}}y^2\,\mathrm{d}y\mathrm{d}x\right)\\
&=4\left(\left[x\right]_{x=0}^{\frac{B}{2}-\frac{b}{2}}\cdot \left[\frac{1}{3}y^3\right]_{y=0}^{\frac{H}{2}}+\left[x\right]_{x= \frac{B}{2}-\frac{b}{2}}^{\frac{B}{2}}\cdot \left[\frac{1}{3}y^3\right]_{y=\frac{h}{2}}^{\frac{H}{2}}\right)\\
&=\frac{BH^3-bh^3}{12}
\end{align*}
\end{document}

This switches between \frac and \tfrac which means if you use \frac in a subscript it might do the wrong thing and use \tfrac it could be made smarter but to be honest. I wouldn't it gets more fragile and it is more robust just to use \tfrac{1}{3} in the original source of you want a third.