ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F12785 on D5521: Riemann sum
Formulation 1
Let $[a, b] \subset \mathbb{R}$ be a D544: Closed real interval such that
(i) \begin{equation} a < b \end{equation}
(ii) $P = ((x_0, x_1, \ldots, x_N), (x^*_1, \ldots, x^*_N))$ is a D5520: Closed real interval tagged partition for $[a, b]$
(iii) $f : [a, b] \to \mathbb{R}$ is a D4364: Real function on $[a, b]$
The Riemann sum for $f$ with respect to $P$ is the D993: Real number \begin{equation} \mathcal{R}_P(f) : = \sum_{n = 1}^N f(x^*_n)(x_n - x_{n - 1}) \end{equation}