Final answer:
The student is seeking to estimate an integral using Gauss-Legendre quadrature, a numerical method to approximate the integral of a function over a specified interval.
Step-by-step explanation:
The student is asking how to use Gauss-Legendre quadrature to estimate the integral I = ∫ from 1 to 3 (x³ + e˥/x˥)dx. This mathematical technique is used for computing the integral of a function when an exact integration is difficult or impossible. To apply Gauss-Legendre quadrature, one must select appropriate weights and abscissas based on the degree of the polynomial that best approximates the function being integrated and the number of points in the desired approximation. Then, the integral is estimated by summing the product of function values at these points with their corresponding weights. However, the provided information seems irrelevant to this question, as it details concepts like odd functions, surface integrals, and Gauss's Law, which do not directly help in computing the quadrature for the given integral.