. Define f: [0, 1] → R by f(x) = r if z is rational and f(x) = 0 if z is irrational. (a) Given any partition P = {0, 1, 2,...,n) of [0, 1], show that U(f, P) > 0.5. (Hint: since z > -1 we have , > (₁+1-1)/2) (b) Show that is not integrable.
. Define f: [0, 1] → R by f(x) = r if z is rational and f(x) = 0 if z is irrational. (a) Given any partition P = {0, 1, 2,...,n) of [0, 1], show that U(f, P) > 0.5. (Hint: since z > -1 we have , > (₁+1-1)/2) (b) Show that is not integrable.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![4. Define f: [0, 1] → R by f(x) = r if z is rational and f(x) = 0 if z is irrational.
(a) Given any partition P= {0, 1, 2,...,n) of [0, 1], show that U(f, P) >
0.5. (Hint: since z > -1 we have r, > (r, +1-1)/2)
(b) Show that is not integrable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e598bbf-2d35-4afb-a9bb-7e240f86d153%2Fe1896223-691d-497e-9110-6721d224bfb0%2Fhkol0wc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Define f: [0, 1] → R by f(x) = r if z is rational and f(x) = 0 if z is irrational.
(a) Given any partition P= {0, 1, 2,...,n) of [0, 1], show that U(f, P) >
0.5. (Hint: since z > -1 we have r, > (r, +1-1)/2)
(b) Show that is not integrable.
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