# Discrete and continuous Centroid equations in LaTeX

I would like to write the following equations in LaTeX:

and

The first one (with the integrals) I managed to make similarly using the following code:

$$COG = \frac{\int_a^b\!ua(x)x\, \mathrm{d}x}{\int_a^b\!ua(x)\, \mathrm{d}x} \label{eq:cogCont}$$


However, I am using a u instead of a μ and have no idea how to do it another way, as well, I do not know how to make the "A" next to it.

For the second equation, I have no idea where to start. Any ideas?

Thanks!

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An exemplary solution. The second label commented.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\def\dint{\displaystyle\int}
\def\dsum{\displaystyle\sum}

$$\mathrm{COG} = \frac{\dint_a^b\!\mu_{A}(x)x\, {d}x}{\dint_a^b\!\mu_{A}(x)\, {d}x} \label{eq:cogCont}$$

$$\mathrm{COG} = \frac{\dsum_{x=a}^b\!\mu_{A}(x)x}{\dsum_{x=a}^b\!\mu_{A}(x)} %\label{eq:cogCont}$$

\end{document}


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