Determine constants a, b, c, d that will produce a quadrature formula 1 [ ƒ(x)dx = af(−1) + bƒ(1) + cf′ (−1) + dƒ' (1) -1 that has degree of precision three. (Hint: Evaluate both sides of the quadrature formula for f(x) = 1, ƒ(x) = x, ƒ(x) = x², ƒ(x) = x³. Solve the resulting system of linear equations.)
Determine constants a, b, c, d that will produce a quadrature formula 1 [ ƒ(x)dx = af(−1) + bƒ(1) + cf′ (−1) + dƒ' (1) -1 that has degree of precision three. (Hint: Evaluate both sides of the quadrature formula for f(x) = 1, ƒ(x) = x, ƒ(x) = x², ƒ(x) = x³. Solve the resulting system of linear equations.)
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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![**Problem Statement:**
Determine constants \(a, b, c, d\) that will produce a quadrature formula
\[
\int_{-1}^{1} f(x) \, dx = af(-1) + bf(1) + cf'(-1) + df'(1)
\]
that has a degree of precision three.
**Hint:** Evaluate both sides of the quadrature formula for \(f(x) = 1\), \(f(x) = x\), \(f(x) = x^2\), \(f(x) = x^3\). Solve the resulting system of linear equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61827b71-1d32-46e9-9f76-5e913a0ea2fb%2F40496ea8-f2cb-43fd-bc84-f545b7e0ea60%2Fs4pa07i_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Determine constants \(a, b, c, d\) that will produce a quadrature formula
\[
\int_{-1}^{1} f(x) \, dx = af(-1) + bf(1) + cf'(-1) + df'(1)
\]
that has a degree of precision three.
**Hint:** Evaluate both sides of the quadrature formula for \(f(x) = 1\), \(f(x) = x\), \(f(x) = x^2\), \(f(x) = x^3\). Solve the resulting system of linear equations.
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