Chapter 4.5, Problem 3ES

a.

To determine

The value of $R_{4,4}$ for the integral ${\displaystyle \underset{1}{\overset{1.5}{\int }}{x}^2\ln x}dx$, using Romberg integration.

b.

To determine

The value of $R_{4,4}$ for the integral ${\displaystyle \underset{0}{\overset{1}{\int }}{x}^2{e}^{-x}}dx$, using Romberg integration.

c.

To determine

The value of $R_{4,4}$ for the integral ${\displaystyle \underset{0}{\overset{0.35}{\int }}\frac{2}{x^2-4}}dx$, using Romberg integration.

d.

To determine

The value of $R_{4,4}$ for the integral ${\displaystyle \underset{0}{\overset{\frac{\pi }{4}}{\int }}{x}^2\sin x}dx$, using Romberg integration.

e.

To determine

The value of $R_{4,4}$ for the integral ${\displaystyle \underset{0}{\overset{\frac{\pi }{4}}{\int }}{e}^{3x}\sin 2x}dx$, using Romberg integration.

f.

To determine

The value of $R_{4,4}$ for the integral ${\displaystyle \underset{1}{\overset{1.6}{\int }}\frac{2x}{x^2-4}}dx$, using Romberg integration.

g.

To determine

The value of $R_{4,4}$ for the integral ${\displaystyle \underset{3}{\overset{3.5}{\int }}\frac{x}{\sqrt{x^2-4}}}dx$, using Romberg integration.

h.

To determine

The value of $R_{4,4}$ for the integral ${\displaystyle \underset{3}{\overset{\frac{\pi }{4}}{\int }}{\left(\cos x\right)}^2}dx$, using Romberg integration.