5. What should be the value of a if the formula [ƒ(x)dx = f(-a) + ƒ (a) is to be exact for (a) all quadratic polynomials. (b) all cubic polynomials. (c) polynomial of the form f(x)= a +bx+cx³ +dx².
5. What should be the value of a if the formula [ƒ(x)dx = f(-a) + ƒ (a) is to be exact for (a) all quadratic polynomials. (b) all cubic polynomials. (c) polynomial of the form f(x)= a +bx+cx³ +dx².
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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Question
answer 5
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.
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