Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
et [a, b] be a real interva b]→X is continuous, the is continuously differentia

et [a, b] be a real interva b]→X is continuous, the is continuously differentia

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
Q.10. (a) Let [a, b] be a real interval and X be a Banach space (i) If f:[a,b] → X is continuous, then prove that F(t)=ff(s)ds is continuously differentiable in (a, b) a and F = f. (ii) If f is continuously differentiable in an open interval containing [a, b], then prove that f(b)-f(a)=f(t)dt
Transcribed Image Text:Q.10. (a) Let [a, b] be a real interval and X be a Banach space (i) If f:[a,b] → X is continuous, then prove that F(t)=ff(s)ds is continuously differentiable in (a, b) a and F = f. (ii) If f is continuously differentiable in an open interval containing [a, b], then prove that f(b)-f(a)=f(t)dt
Expert Solution
steps

Step by step

Solved in 2 steps with 2 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