What Happens When You Integrate the Square of the Delta Function Over All Space?

[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.