Integral of the square of the Dirac delta function

[bishshoy007]

Homework Statement

$$\int \delta(t)^{2}$$ dt from -infinity to +infinty

Homework Equations

$$\int^{\infty}_{-\infty}\delta(t)dt = 1$$

$$\int uv dt = u\int v dt - \int u^{'}(t)\int v dt dt$$

$$\int^{b}_{a} f(x) dx = F(b) - F(a)$$

$$\delta(-\infty) = \delta(\infty) = 0$$

The Attempt at a Solution

$$\int \delta(t) . \delta(t) dt = \delta(t)\int \delta(t) dt - \int \frac{d \delta(t)}{dt} . \int \delta(t) dt dt = \delta(t).1 - \int \frac{d \delta(t)}{dt}dt = \delta(t) - \delta(t) = 0$$

 

[Dick]

The integral of delta(x)^2 is not defined, it's infinite. Is that really the problem you were given?

 

[bishshoy007]

The integral of delta(x)^2 is not defined, it's infinite. Is that really the problem you were given?

Thank you for replying.
$$\delta(t)$$ is an energy signal. I'm trying to find out the energy of the signal.
I wonder why the integral came out to be zero. I want some expert advice, whether I have done the integral correctly or not, or if there is some other explanations.

 

[bishshoy007]

anybody please answer to my problem.
why the integral turns out to be zero.