Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let f: [a, b] → R be a bounded function. Then f [a, b] → R is Riemann integrable if and only if there is a sequence {Pn} of partitions of [a, b] such that lim (U(f, Pn) - L(f, Pn)) = 0. nx In this case, the Riemann integral of f over [a, b] can be computed by S f = a lim L(f, Pn) = lim U(f, Pn). n4x n→∞ (4.1) (4.2)

Let f: [a, b] → R be a bounded function. Then f [a, b] → R is Riemann integrable if and only if there is a sequence {Pn} of partitions of [a, b] such that lim (U(f, Pn) - L(f, Pn)) = 0. nx In this case, the Riemann integral of f over [a, b] can be computed by S f = a lim L(f, Pn) = lim U(f, Pn). n4x n→∞ (4.1) (4.2)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

please prove every step and don't use other one's answer thank yoi

Let f [a, b] → R be a bounded function. Then f [a, b] → R is Riemann ! integrable if and only if there is a sequence {Pn} of partitions of [a, b] such that lim (U(f, Pn) L(f, Pn)) = 0. (4.1) n→∞ In this case, the Riemann integral of f over [a, b] can be computed by a 1 = lim L(f, Pn) n-x = lim U(f, Pn). n→∞ (4.2)
Transcribed Image Text:Let f [a, b] → R be a bounded function. Then f [a, b] → R is Riemann ! integrable if and only if there is a sequence {Pn} of partitions of [a, b] such that lim (U(f, Pn) L(f, Pn)) = 0. (4.1) n→∞ In this case, the Riemann integral of f over [a, b] can be computed by a 1 = lim L(f, Pn) n-x = lim U(f, Pn). n→∞ (4.2)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 59 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS