3. Derive the following Newton-Cotes formula. 1 (a) f f(x) dx ≈ A₂. = AS (-=-1) + AS ( 1 ) Af -1 2 (b) f(x) dx ≈ Af (0)+ ƒ(1)+ ‚ƒ(2). ƒ 0
3. Derive the following Newton-Cotes formula. 1 (a) f f(x) dx ≈ A₂. = AS (-=-1) + AS ( 1 ) Af -1 2 (b) f(x) dx ≈ Af (0)+ ƒ(1)+ ‚ƒ(2). ƒ 0
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
answer 3
Transcribed Image Text:3. Derive the following Newton-Cotes formula.
(a) f(x)dx = AS (²= ² ) + AS (-
2
2
(b)
-1
j
†ƒ (x)dx = 4ƒ (0) + 4‚ƒ (1) + 4‚ƒ (2).
5. What should be the value of a if the formula [f(x)dx= f(-a) + f(a) is to be exact for
(a) all quadratic polynomials
(b) all cubic polynomials.
(c) polynomial of the form f(x) = a +bx=cx³ + dx²¹.
Expert Solution
Ideas
These are quadrature type approximation. These hold exactly for polynomial of certain degree and else yield an error.
Step by step
Solved in 3 steps with 2 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,
