### Defining your own Control Sequences in LaTeX

Suppose that we are producing a paper that makes frequent
use of some mathematical expression. For example,
suppose that integrals like

occur frequently throughout the text. This formula is
obtained by typing
\[ \int_{-\infty}^{+\infty} f(x)\,dx.\]

It would be nice if we could type `\inftyint`

(say)
to obtain the integral sign at the beginning. This can
be done using `\newcommand`

. What we do is to place
a line with the command
\newcommand{\inftyint}{\int_{-\infty}^{+\infty}}

near the beginning of the input file (e.g., after
the `\documentclass`

command but before the
`\begin{document}`

command). Then we only have to
type
\[ \inftyint f(x)\,dx.\]

to obtain the above formula.
We can modify this procedure slightly. Suppose that we
we defined a new control sequence `\intwrtx`

by
putting the line

\newcommand{\intwrtx}[1]{\int_{-\infty}^{+\infty} #1 \,dx}

at the beginning of the input file. If we then type the line
\[ \intwrtx{f(x)}.\]

then we obtain

What has happened is that the expression in braces
after `\intwrtx`

has been substituted in the expression
defining `\intwrtx`

, replacing the `#1`

in that
expression.
The number 1 inside square brackets in the
`\newcommand`

line defining `\intwrtx`

indicates
to LaTeX that it is to expect one expression (in braces)
after `\intwrtx`

to substitute for `#1`

in the definition of `\intwrtx`

. If we defined a
control sequence `\intwrt`

by

\newcommand{\intwrt}[2]{\int_{-\infty}^{+\infty} #2 \,d #1}

then it would expect two expressions to substitute in for
`#1`

and `#2`

in the definition of `\intwrt`

.
Thus if we then type
\[ \intwrt{y}{f(y)}.\]

we obtain