Chapter 4.7, Problem 1ES

Approximate the following integrals using Gaussian quadrature with n = 2 and compare your results to the exact values of the integrals.

1. a. ${\displaystyle {\int }_1^{1.5}{x}^2}\ln xdx$
2. b. ${\displaystyle {\int }_0^1{x}^2}{e}^{-x}dx$
3. c. ${\displaystyle {\int }_0^{0.35}\frac{2}{x^2-4}}dx$
4. d. ${\displaystyle {\int }_0^{\pi /4}{x}^2}\sin xdx$