- #1
bishshoy007
- 7
- 0
Homework Statement
[tex]\int \delta(t)^{2} [/tex] dt from -infinity to +infinty
Homework Equations
[tex]\int^{\infty}_{-\infty}\delta(t)dt = 1[/tex]
[tex]\int uv dt = u\int v dt - \int u^{'}(t)\int v dt dt[/tex]
[tex] \int^{b}_{a} f(x) dx = F(b) - F(a) [/tex]
[tex]\delta(-\infty) = \delta(\infty) = 0 [/tex]
The Attempt at a Solution
[tex]\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 [/tex]