$How should I approach this question?$

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$How should I approach this question?$

Hello,

I'm not looking for any solutions here but rather I’m having difficulty figuring out how I should properly approach this question…

Using a Gaussian Quadrature of order 5 to approximate

$\int_{2}^{6} \frac4{x-1} \;\mathrm{d}x $

Ordinary Differential Equations

Dmitiri Naoufal

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Divide the interval $[2,6]$ into 6 equal intervals with the end points
\[x_k=2+\frac{4}{6}(i-1), k=1,2,3,4,5,6.\]
Define
\[L_i(x)=\prod_{k=1, k\neq i}^{6}\frac{x-x_i}{x_k -x_i},\]
which is a polynomial of degree 5, and let
\[w_i=\int_{2}^{6}L_i(x)dx.\]
Then
\[\int_{2}^{6}\frac{4}{x-1} dx= \sum_{i=1}^{6}w_i \frac{4}{x_i-1}.\]
See: https://www.dam.brown.edu/people/alcyew/handouts/GLquad.pdf

Erdos

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Dmitiri Naoufal

0

Wouldn’t it be Sum 5 instead of Sum 6?
Erdos

0

No, there are 6 Gaussian Quadrature of order 5 and we should sum over all. The number of terms is always one more than the degree of the polynomial.
Erdos

0

I would say the bounty for your other question is low. It may take about 45 min to an hour to answer the question without using any software.

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