# What is a dummy variable (in an integral)?

## 1 answer

+2

−0

When integrating, a dummy variable is one that "disappears completely in the final result."

For example, in the expression $\int x\ \mathrm{d}x$, $x$ is *not* a dummy variable because the expression is equivalent to $\frac{x^2}{2}+c$, that is, the $x$ hasn't "disappeared." If we had replaced $x$ with, say, $y$, then the result would change (to $\frac{y^2}{2}+c$).

But in the expression you wrote, $x$ is a dummy variable because the expression is equivalent to $\Gamma[n]$, and the $x$ has "disappeared." If we had replaced $x$ with, say, $y$, then the result would not change (it would still be $\Gamma[n]$).

(Note that statistics has a different meaning for the term dummy variable.)

## 1 comment thread