Definition 7.1.3: Riemann Sums
If
P = { x0, x1, x2, ..., xn}
is a partition of the closed interval [a, b] and
f is a function defined on that interval, then the
n-th Riemann Sum of f with respect to
the partition P is defined as:
R(f, P) = f(tj) (xj - xj-1)where tj is an arbitrary number in the interval [xj-1, xj].
Note: If ti is always the left endpoint of each subinterval, the corresponding Riemann sum is called left Riemann sum; if it is always the right endpoint, the sum is called right Riemann sum.