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5. Implement the Gauss-Legendre Quadrature rule with N nodes. For the computation of the quadrature nodes and weights of the Gauss-Legendre quadrature rule use the PYTHON module numpy.polynomial. legendre.leggauss. Test your function by showing its exactness is at least 1 for N = 1 and one interval: f 2xdx = 1 exactly. If the exactness is not at least 1, fix your code. - Fill in the following table by computing the integrals over [0, 1] of the indicated integrands using your code. It is given that the degree of exactness of the method is 2N-1. Error for N = 2 Error for N = 3 f 3x² 42-3 524 625 7.26 Degree

5. Implement the Gauss-Legendre Quadrature rule with N nodes. For the computation of the quadrature nodes and weights of the Gauss-Legendre quadrature rule use the PYTHON module numpy.polynomial. legendre.leggauss. Test your function by showing its exactness is at least 1 for N = 1 and one interval: f 2xdx = 1 exactly. If the exactness is not at least 1, fix your code. - Fill in the following table by computing the integrals over [0, 1] of the indicated integrands using your code. It is given that the degree of exactness of the method is 2N-1. Error for N = 2 Error for N = 3 f 3x² 42-3 524 625 7.26 Degree

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Please do question 6 (it is in the photo) with python coding. 

6. Implement the Gauss-Legendre Quadrature rule with N nodes. For the computation of the quadrature nodes and weights of the Gauss-Legendre quadrature rule use the PYTHON module numpy.polynomial. legendre.leggauss. Test your function by showing its exactness is at least 1 for N = 1 and one interval: 2xdx = 1 exactly. If the exactness is not at least 1, fix your code. - Fill in the following table by computing the integrals over [0, 1] of the indicated integrands using your code. It is given that the degree of exactness of the method is 2N - 1. Error for N = 2 Error for N = 3 f 3.x² 4.2.3 5x4 6.7-5 7.2-6 Degree
Transcribed Image Text:6. Implement the Gauss-Legendre Quadrature rule with N nodes. For the computation of the quadrature nodes and weights of the Gauss-Legendre quadrature rule use the PYTHON module numpy.polynomial. legendre.leggauss. Test your function by showing its exactness is at least 1 for N = 1 and one interval: 2xdx = 1 exactly. If the exactness is not at least 1, fix your code. - Fill in the following table by computing the integrals over [0, 1] of the indicated integrands using your code. It is given that the degree of exactness of the method is 2N - 1. Error for N = 2 Error for N = 3 f 3.x² 4.2.3 5x4 6.7-5 7.2-6 Degree
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How will the output look for this particular code:

def leggauss_ab(n=2, a=0, b=1):

  assert(n>0)

  x,w = numpy.polynomial.legendre.leggauss(n)

  x = (b-a) * 0.5 *x+(b+a)*0.5

  w = w * (b-a) * 0.5

  return x,w 

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