Suppose I want to evaluate \begin{align} \int^{T}_0{e^{-t}x(t)dt}. \end{align} However, I can only approximate the continuous function $\mathbb{R}_+ \ni t \mapsto x(t)$ by a discrete sequence $\{x_t : t \in \{0,\Delta t, 2\Delta t, \ldots,T\}\}$.
- Is the following true (given $T \to \infty$ and $\Delta t \to 0$)? \begin{align} \int^T_0{e^{-t}x(t)dt} \approx \sum^{T}_{t=0}{e^{-t}x_t\Delta dt} \end{align}
