Btukfyl

I have an equation where I integrate over $lambda$ from 85deg to 95deg and 265deg to 275deg (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}}

begin{equation}

mathrm{x}_i=frac{int_{85deg, 265deg}^{95deg, 275deg}int_{-90deg}^{90deg}

cos{left(deltaright)}mathrm{x}_{i,delta,lambda}

mathrm{d}deltamathrm{d}lambda}

{int_{0deg}^{360deg}int_{-90deg}^{90deg}

cos{left(deltaright)}

mathrm{d}deltamathrm{d}lambda},

end{equation}

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 85deg,text{to},95deg and 265deg,text{to},275deg are too "wordy,'' you could switch to 90degpm5deg and 270degpm5deg.

documentclass{article}

usepackage{amsmath}

renewcommand{deg}{ensuremath{^circ}}

newcommandddfrac[2]{dfrac{displaystyle #1}{displaystyle #2}} % "double display style"

letsssscriptscriptstyle % handy shorthand macro

begin{document}

begin{align*}

mathrm{x}_i

&=frac{int_{85deg, 265deg}^{95deg, 275deg}int_{-90deg}^{90deg}

cos{left(deltaright)}mathrm{x}_{i,delta,lambda}

mathrm{d}deltamathrm{d}lambda}

{int_{0deg}^{360deg}int_{-90deg}^{90deg}

cos{left(deltaright)}

mathrm{d}deltamathrm{d}lambda}quadtext{``before''}\[4ex]

&=ddfrac{

int_{!substack{sss85deg,text{to},95deg\

                  sss265deg,text{to},275deg}}

int_{!-pi/2}^{pi/2}

cos(delta) mathrm{x}^{}_{i,delta,lambda}

,mathrm{d}delta,mathrm{d}lambda}%

{int_{0}^{2pi}

int_{!-pi/2}^{pi/2}

cos(delta)

,mathrm{d}delta,mathrm{d}lambda}quadtext{``after''}

end{align*}

end{document}