How to determine the power of a finite signal?
First of all, note that your formula for signal power is only valid for real-valued $x(t)$ that satisfy $x(t)=0$ for $t&lt;0$.

A more general formula is

$$P_x=\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^{T}|x(t)|^2dt\tag{1}$$

For signals with finite energy

$$E_x=\int_{-\infty}^{\infty}|x(t)|^2dt\lt\infty\tag{2}$$

the power $P_x$ defined by $(1)$ is clearly zero.