Interactive Real Analysis
- part of Definition 7.1.8: The Riemann Integral
Suppose f is a bounded function defined on a closed, bounded interval
. Define the upper and lower Riemann
integrals, respectively, as
Context
I*(f) = inf{ U(f,P): P a partition of [a, b]}Then if I*(f) = I*(f) the function f is called Riemann integrable and the Riemann integral of f over the interval [a, b] is denoted by
I*(f) = sup{ L(f,P): P a partition of [a, b]}
f(x) dx
Context