What are the units of A and δ in Dirac's delta function?

[Gonzolo]

Consider :

$$E = \int P(\tau) d\tau = \int A\delta(\tau) d\tau$$

E is in Joules and $$P(\tau)$$ is in Watts, what are the units of A? What about $$\delta$$?

I have a hunch, but need to have all doubts removed.

 

[mathman]

The delta function has the dimension of the reciprocal of the variable of integration. Thus delta(tau)d(tau) is non-dimensional. Therefore A has the same dimension as E, i.e. Joules.

 

[Gokul43201]

And you can see why the dirac delta has units of the reciprocal of the integration variable from

$$\int _{-\infty} ^{\infty} \delta (p-p_0) dp = 1$$,
where p is any parameter.

 

[Gonzolo]

Thanks guys!