Chapter 4.7, Problem 4ES

Repeat Exercise 2 with n = 3.

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

1. a. ${\displaystyle {\int }_0^{\pi /4}{e}^{3x}\sin 2xdx}$
2. b. ${\displaystyle {\int }_1^{1.6}\frac{2x}{x^2-4}dx}$
3. c. ${\displaystyle {\int }_3^{3.5}\frac{x}{\sqrt{x^2-4}}dx}$
4. d. ${\displaystyle {\int }_0^{\pi /4}{(\cos x)}^{2}dx}$