Fourier transform formulation of the dirac delta

1. Aug 1, 2007

ehrenfest

I have seen two formulations of the dirac delta function with the Fourier transform. The one on wikipedia is
$$\int_{-\infty}^\infty 1 \cdot e^{-i 2\pi f t}\,dt = \delta(f)$$

and the one in my textbook (Robinett) is

$$1/2\pi \int_{-\infty}^\infty 1 \cdot e^{-i f t}\,dt = \delta(f)$$

I do not understand how they are equivalent? How can you just take the 2pi out of the integral?

2. Aug 1, 2007

George Jones

Staff Emeritus
It's a simple change of variable: if $t'=2\pi t$, then $dt=dt'/2\pi$.