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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Concept explainers
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09aab431-c4ff-4ffe-8b86-36e6b75dfb4d%2F2b775f82-5a41-4730-9502-b9aa38b35c08%2Fexor2g5_processed.jpeg&w=3840&q=75)
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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