| Problem Set |
Chapter |
Problems |
|---|---|---|
| 29 | ∗44 | Using a machine on which Mathematica is installed, download and open up this notebook. Its purpose is to illustrate the simple functions of Theorem 11.20 building up to a nonnegative function f. Compute the integrals IA(sn) for n = 1, 2, 5, 8, where A is the interval [-2, 2]. (You may use Mathematica's Integrate or NIntegrate command in the process; do it for the simple functions that arise from the function f that is defined in the notebook.) Compute also the integral of f over this same A. |
| ∗45 | At about the time when we got Theorem S.35 (or whatever we called the next Theorem after Thm. 7.15 in the notes), we reviewed the meaning of the phrase “f is Riemann-integrable on the interval [a, b].” Let A be the intersection of the rational numbers with the interval [0, 1] (subset of the real line). Show that the characteristic function χA is not Riemann-integrable on [0, 1]. | |
| n | manditory problem |
| ∗n | manditory problem, not from text |
| (n) | helper problem |
| [n] | ungraded problem |
| [∗n] | ungraded problem, not from text |
| {n} | optional problem |