Let RI be the set of functions that are Riemann Integrable.
Disprove with a counterexample or prove the following true.
(a) f in RI implies |f| in RI
(b) |f| in RI implies f in RI
(c) f in RI and 0 < c <= |f(x)| forall x implies 1/f in RI
(d) f in RI implies f^2 in RI
(e) f^2 in RI implies f in RI
(f) f^3 in RI implies f in RI© BrainMass Inc. brainmass.com October 9, 2019, 8:32 pm ad1c9bdddf
Proof: Let and . Then . Since
is Riemann integrable, then both and are Riemann integrable. Thus is also Riemann integrable. Hence belongs to RI.
For example, we consider defined as if ...
Riemann integrability is investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.