(4) Suppose f(x) is increasing on [a,b]. Let P₁ = {xo, ₁,...,n}, where xk = a + k (b − a), k = 0, 1,..., n. Prove that and [ f(x) dx 0 ≤ U(³Pm S) - fº f(x) dx ≤ b=ª (ƒ(1) — S (a)) n = lim U(Pn, f). 8个
(4) Suppose f(x) is increasing on [a,b]. Let P₁ = {xo, ₁,...,n}, where xk = a + k (b − a), k = 0, 1,..., n. Prove that and [ f(x) dx 0 ≤ U(³Pm S) - fº f(x) dx ≤ b=ª (ƒ(1) — S (a)) n = lim U(Pn, f). 8个
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![(4) Suppose f(x) is increasing on [a, b]. Let Pn
[a, b]. Let P₁ = {0, ₁,...,n}, where x = a + (b − a),
k/2
n
k = 0, 1, . . . , n. Prove that
9.9
[1(2)
and
b
- [* F(x) dx ≤ b = ª (f(0) - F(a))
f(x²)
a (ƒ(b)
<
N
0 ≤ U(Pn, f) -
f(x) dx lim U(Pn, f).
n→∞
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a04a0c8-a6a9-473e-b4ed-0840bde177a1%2F11037c94-0031-4d45-8c68-d8e481d02440%2Fd5pjbf8_processed.png&w=3840&q=75)
Transcribed Image Text:(4) Suppose f(x) is increasing on [a, b]. Let Pn
[a, b]. Let P₁ = {0, ₁,...,n}, where x = a + (b − a),
k/2
n
k = 0, 1, . . . , n. Prove that
9.9
[1(2)
and
b
- [* F(x) dx ≤ b = ª (f(0) - F(a))
f(x²)
a (ƒ(b)
<
N
0 ≤ U(Pn, f) -
f(x) dx lim U(Pn, f).
n→∞
=
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
