# Integral over two ranges [closed]

I have an equation where I integrate over $\lambda$ from 85\deg to 95\deg and 265\deg to 275\deg (ie. just at 90 and 270 with 5 degrees on either side. I'm wondering if there's a convenient way of notating this other than two separate integrals added together. I wrote a solution below, but my question is whether that's a mathematically standard way of writing this and if there's a better way. Thanks!

\providecommand{\deg}{}
\renewcommand{\deg}{\ensuremath{^\circ}}
$$\mathrm{x}_i=\frac{\int_{85\deg, 265\deg}^{95\deg, 275\deg}\int_{-90\deg}^{90\deg} \cos{\left(\delta\right)}\mathrm{x}_{i,\delta,\lambda} \mathrm{d}\delta\mathrm{d}\lambda} {\int_{0\deg}^{360\deg}\int_{-90\deg}^{90\deg} \cos{\left(\delta\right)} \mathrm{d}\delta\mathrm{d}\lambda},$$


## closed as off-topic by user36296, Mensch, Phelype Oleinik, Circumscribe, Money Oriented ProgrammerJan 8 at 23:09

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question does not fall within the scope of TeX, LaTeX or related typesetting systems as defined in the help center." – user36296, Mensch, Phelype Oleinik, Circumscribe, Money Oriented Programmer
If this question can be reworded to fit the rules in the help center, please edit the question.

• Welcome (back) to TeX.SE! Questions about best practises in mathematical notation are mostly off-topic for this site, you will probably get better answers on math.stackexchange.com. Of course, if you find a notation and you don't know how to render it in LaTeX, you can ask it here. – Marijn Jan 8 at 21:37
• For sure, to avoid code clutter, please write \cos(\delta) instead of \cos{\left(\delta\right)}. – Mico Jan 8 at 22:19

I can't help with the mathematically standard way for writing the expression at hand -- assuming there even is a "standard way".

From a typographical point of view, though, i.e., from the point of view of making the expression reasonably easy to parse and understand, I'd say it would make sense to re-write the two ranges of integration of the first integral using the \substack macro of the amsmath package. I would also cast both the numerator and the denominator in display-style math mode.

For the limits of integration of the 2nd thru 4th integrals, I think it's ok to use radians-style notation. Anyone who is able to follow the rest of your paper shouldn't be thrown off by an in-equation switch from degrees notation to radians notation, right?

Remark: If you believe that 85\deg\,\text{to}\,95\deg and 265\deg\,\text{to}\,275\deg are too "wordy,'' you could switch to 90\deg\pm5\deg and 270\deg\pm5\deg.

\documentclass{article}
\usepackage{amsmath}
\renewcommand{\deg}{\ensuremath{^\circ}}
\newcommand\ddfrac[2]{\dfrac{\displaystyle #1}{\displaystyle #2}} % "double display style"
\let\sss\scriptscriptstyle % handy shorthand macro
\begin{document}
\begin{align*}
\mathrm{x}_i
&=\frac{\int_{85\deg, 265\deg}^{95\deg, 275\deg}\int_{-90\deg}^{90\deg}
\cos{\left(\delta\right)}\mathrm{x}_{i,\delta,\lambda}
\mathrm{d}\delta\mathrm{d}\lambda}
{\int_{0\deg}^{360\deg}\int_{-90\deg}^{90\deg}
\cos{\left(\delta\right)}
\mathrm{d}\delta\mathrm{d}\lambda}\quad\text{before''}\\[4ex]
&=\ddfrac{
\int_{\!\substack{\sss85\deg\,\text{to}\,95\deg\\
\sss265\deg\,\text{to}\,275\deg}}
\int_{\!-\pi/2}^{\pi/2}
\cos(\delta) \mathrm{x}^{}_{i,\delta,\lambda}
\,\mathrm{d}\delta\,\mathrm{d}\lambda}%
{\int_{0}^{2\pi}
\int_{\!-\pi/2}^{\pi/2}
\cos(\delta)
\,\mathrm{d}\delta\,\mathrm{d}\lambda}\quad\text{after''}
\end{align*}
\end{document}