Area under the dirac-delta function

Question

I am having a problem understanding dirac-delta distribution. Why the strength of the pulse is equal to the area under it?

Is the strength the pick value of the delta distribution, if so how can it be equal to the area under it?

Answer 1

Since $\delta(x) = \infty $ when $x = 0$ , otherwise $\delta(x)= 0$ , there is no finite peak value. However $\int \delta(x) dx = 1$ which is the area under $\delta(x)$ and so we might consider $1$ to be the strength. Then if we increase the 'strength' by c, that is, $c\int \delta(x) dx = c $ , we can see the new strength is equal to the new area.