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What is the best way to show that a variable is the outcome of an average, assuming that I am talking about reflectance value in spectral interval between two wavelenghts:

$$ Averaged\, Value = \frac{1}{\lambda_{f} -\lambda_{i}} \cdot \int_{\lambda_{i}}^{\lambda_{f}} \lambda d\lambda
$$

enter image description here

$$
\overline{R} = \frac{1}{\lambda_{f} -\lambda_{i}} \cdot \int_{\lambda_{i}}^{\lambda_{f}} \lambda d\lambda
$$

enter image description here

G M
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    never use math italic for words the font is designed to make it not look like a word but a product of variables. \text{Averaged Value} not Averaged\, Value – David Carlisle Jan 09 '17 at 10:40
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    two comments, neither relevant to purpose of question: better to use \[...\] rather than $$ (Why is \[ … \] preferable to $$?), and use \mathit{Averaged Value} because these are words, not a string of variables (a basic principle regarding words vs. variables). – barbara beeton Jan 09 '17 at 10:40
  • In math, it better to use a symbol instead of two words. For average it is better to use the \bar not the \overline: \bar{R} https://i.stack.imgur.com/2z6Nl.png – Oren Ben-Harim Jun 27 '19 at 04:37

2 Answers2

13

I start from the assumption that readers can read, so there's no point in stating twice what you're talking about. If you don't need the quantity later, just state the value, otherwise define a symbol for it.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

The averaged value of reflectance in the spectral interval between two wavelengths is
\[
\frac{1}{\lambda_{f} -\lambda_{i}} \int_{\lambda_{i}}^{\lambda_{f}} \lambda\, d\lambda
\]

The averaged value $\overline{R}$ of reflectance $R$ in the spectral
interval between two wavelengths is
\[
\overline{R}=
\frac{1}{\lambda_{f} -\lambda_{i}} \int_{\lambda_{i}}^{\lambda_{f}} \lambda\, d\lambda
\]

\end{document}

enter image description here

egreg
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0

For the average of p(t) over T, I would propose:

$$P = {\left.\overline{p(t)}\right|_0^T}$$

in preference of

$$P = \frac{1}{T}\int_0^T p(t)\ \d t.$$

The reason being that the integration sign is intimidating for people without a mathematical background. See:

comparison

skvery
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