Note: If you have already answered this exact question please do not answer it again. I would like an answer from a different T.A. Thanks
Say abs = absolute value.
Suppose that the function f:[a,b]->R is Lipschitz;
that is , there is a number c such that:
abs(f(u) - f(v)) <= (c)abs(u-v)
for all u and v in [a,b]. Let P be a partition of [a,b] and R(f,P) be a Riemann sum based on P. Prove that
abs((R(f,P)) - (the integral from a to b of f)) <= ||P||(b-a)© BrainMass Inc. brainmass.com November 29, 2021, 11:57 pm ad1c9bdddf
Please see the attachement.
<br>I am not very clear of ||P||.
Proof: Since ...
An analysis proof for an absolute value is found. The partition of a Riemann sum based on a function is given.