Chapter 4.4, Problem 5ES

a.

To determine

To approximate: The value of the integral ${\displaystyle \underset{1}{\overset{2}{\int }}x\ln xdx},n=4$ using the composite Midpoint rule with $n+2$ sub intervals.

b.

To determine

To approximate: The value of the integral ${\displaystyle \underset{-2}{\overset{2}{\int }}{x}^3{e}^{x}dx},n=4$ using the composite Midpoint rule with $n+2$ sub intervals.

c.

To determine

To approximate: The value of the integral ${\displaystyle \underset{0}{\overset{2}{\int }}\frac{2}{x^2+4}dx},n=6$ using the composite Midpoint rule with $n+2$ sub intervals.

d.

To determine

To approximate: The value of the integral ${\displaystyle \underset{0}{\overset{\pi }{\int }}{x}^2\cos xdx},n=6$ using the composite Midpoint rule with $n+2$ sub intervals.

e.

To determine

To approximate: The value of the integral ${\displaystyle \underset{0}{\overset{2}{\int }}{e}^{2x}\sin 3xdx},n=8$ using the composite Midpoint rule with $n+2$ sub intervals.

f.

To determine

To approximate: The value of the integral ${\displaystyle \underset{1}{\overset{3}{\int }}\frac{x}{x^2+4}dx},n=8$ using the composite Midpoint rule with $n+2$ sub intervals.

g.

To determine

To approximate: The value of the integral ${\displaystyle \underset{3}{\overset{5}{\int }}\frac{1}{\sqrt{x^2-4}}dx},n=8$ using the composite Midpoint rule with $n+2$ sub intervals.

h.

To determine

To approximate: The value of the integral ${\displaystyle \underset{0}{\overset{\frac{3\pi }{8}}{\int }}\tan xdx},n=8$ using the composite Midpoint rule with $n+2$ sub intervals.