Consider the following integral:
$$\mathcal{I}=\int\limits_0^0 \{x\}^{\lfloor x\rfloor}\,\mathrm dx$$
Now, my concern is that at $x=0$, the value of the integrand is $0^0$ which is undefined.
It's obvious that the Cauchy principal value of $\mathcal I$ is $0$, but what would the value of the integral be in general sense? $0$ or undefined?
Clarification: $\{\cdot\}$ is the fractional part function and $\lfloor \cdot\rfloor$ is the floor function.
Thanks in advance! :)