Interactive Real Analysis
- part of Definition 7.1.5: Upper and Lower Sum
Let
P = { x0, x1, x2, ..., xn}
be a partition of the closed interval [a, b] and
f a bounded function defined on that interval. Then:
Context
The upper sum of f with respect to the partition P is defined as:
U(f, P) =where cj is the supremum of f(x) in the interval [xj-1, xj].cj (xj - xj-1)
The lower sum of f with respect to the partition P is defined as
L(f, P) =where dj is the infimum of f(x) in the interval [xj-1, xj].
Context