Chapter 4.5, Problem 4ES

a.

To determine

The value of $R_{4,4}$ for the integral ${\displaystyle \underset{-1}{\overset{1}{\int }}{\left(\cos x\right)}^2}dx$, using Romberg integration.

b.

To determine

The value of $R_{4,4}$ for the integral ${\displaystyle \underset{-0.75}{\overset{0.75}{\int }}x\left(\ln \left(x+1\right)\right)}dx$, using Romberg integration.

c.

To determine

The value of $R_{4,4}$ for the integral ${\displaystyle \underset{1}{\overset{4}{\int }}\left({\left(\sin x\right)}^2-2x\sin x+1\right)}dx$, using Romberg integration.

d.

To determine

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