Suppose we seek a numerical integration formula of the form | f(2)da = af(4) + bf(5.2) + ef(6.4) + df(7) + E(f) where the error term E(f) is equal to zero if f(x) is a polynomial of degree at most three. To find coefficients a, b, c, and d, we use method of undetermined coefficients. • ith f(x) = 1 we get the linear equation • With f(x) = x – - 4 we get the linear equation • With f(x) = (x – 4) we get the linear equation - • With f(æ) = (x – 4)° we get the linear equation - Solving the system of linear equations, based on the above four equations, answer the following questions: 1. What is the coefficient a ? 2. What is the coefficient b ? 3. What is the coefficient c? 4. What is the coefficient d?
Suppose we seek a numerical integration formula of the form | f(2)da = af(4) + bf(5.2) + ef(6.4) + df(7) + E(f) where the error term E(f) is equal to zero if f(x) is a polynomial of degree at most three. To find coefficients a, b, c, and d, we use method of undetermined coefficients. • ith f(x) = 1 we get the linear equation • With f(x) = x – - 4 we get the linear equation • With f(x) = (x – 4) we get the linear equation - • With f(æ) = (x – 4)° we get the linear equation - Solving the system of linear equations, based on the above four equations, answer the following questions: 1. What is the coefficient a ? 2. What is the coefficient b ? 3. What is the coefficient c? 4. What is the coefficient d?
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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Transcribed Image Text:Suppose we seek a numerical integration formula of the form
| f(2)da = af(4) + bf(5.2) + ef(6.4) + df(7) + E(f)
where the error term E(f) is equal to zero if f(x) is a polynomial of degree at most three. To find
coefficients a, b, c, and d, we use method of undetermined coefficients.
• With f(x) = 1 we get the linear equation
• With f(x) = x –
- 4 we get the linear equation
• With f(x) = (x – 4) we get the linear equation
-
• With f(æ) = (x – 4)° we get the linear equation
-
Solving the system of linear equations, based on the above four equations, answer the following questions:
1. What is the coefficient a ?
2. What is the coefficient b ?
3. What is the coefficient c?
4. What is the coefficient d?
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