Chapter 4.5, Problem 1ES

Use Romberg integration to compute R_{3, 3} for the following 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. ${\displaystyle {\int }_0^{\pi /4}{x}^2}\sin xdx$
5. e. ${\displaystyle {\int }_0^{\pi /4}{e}^{3x}}\sin 2xdx$
6. f. ${\displaystyle {\int }_1^{1.6}\frac{2x}{x^2-4}}dx$
7. g. ${\displaystyle {\int }_3^{3.5}\frac{x}{\sqrt{x^2-4}}}dx$
8. h. ${\displaystyle {\int }_0^{\pi /4}{(\cos x)}^2}dx$