Use the above to evaluate x sin(x) ap: - 72

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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part c only

Gaussian quadrature:
Find the first three monic polynomials (i.e., till quadratic) on [0, 1] orthogonal with respect
to the inner product
(f, 9) =
f(x)g(x)dx
Use the above to find a quadrature formula of the form
n
f (x)dx = a;f(x;)
1 -
i=0
that is exact for all f(x) of degree 3.
a sin(x)
Use the above to evaluate
xp:
V1- x2
2.
Transcribed Image Text:Gaussian quadrature: Find the first three monic polynomials (i.e., till quadratic) on [0, 1] orthogonal with respect to the inner product (f, 9) = f(x)g(x)dx Use the above to find a quadrature formula of the form n f (x)dx = a;f(x;) 1 - i=0 that is exact for all f(x) of degree 3. a sin(x) Use the above to evaluate xp: V1- x2 2.
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