Chapter 4.3, Problem 9ES

(a)

To determine

The value of the integral ${\displaystyle \underset{0.5}{\overset{1}{\int }}{x}^{4}dx}$ using Midpoint rule.

(b)

To determine

The value of the integral ${\displaystyle \underset{0}{\overset{0.5}{\int }}\frac{2}{x-4}dx}$ using Midpoint rule.

(c)

To determine

The value of the integral ${\displaystyle \underset{1}{\overset{1.5}{\int }}{x}^2\ln xdx}$ using Midpoint rule.

(d)

To determine

The value of the integral ${\displaystyle \underset{0}{\overset{1}{\int }}{x}^2{e}^{-x}dx}$ using Midpoint rule.

(e)

To determine

The value of the integral ${\displaystyle \underset{1}{\overset{1.6}{\int }}\frac{2x}{x^2-4}dx}$ using Midpoint rule.

(f)

To determine

The value of the integral ${\displaystyle \underset{0}{\overset{0.35}{\int }}\frac{2}{x^2-4}dx}$ using Midpoint rule.

(g)

To determine

The value of the integral ${\displaystyle \underset{0}{\overset{\frac{\pi }{4}}{\int }}x\sin xdx}$ using Midpoint rule.

(h)

To determine

The value of the integral ${\displaystyle \underset{0}{\overset{\frac{\pi }{4}}{\int }}{e}^{3x}\sin 2xdx}$ using Midpoint rule.