Chapter 4.3, Problem 10ES

(a)

To determine

The value of the integral ${\displaystyle \underset{-0.25}{\overset{0.25}{\int }}{\left(\cos x\right)}^{2}dx}$ using Midpoint rule.

(b)

To determine

The value of the integral ${\displaystyle \underset{-0.5}{\overset{0}{\int }}x\ln \left(x+1\right)dx}$ using Midpoint rule.

(c)

To determine

The value of the integral ${\displaystyle \underset{0.75}{\overset{1.3}{\int }}\left({\left(\sin x\right)}^2-2x\sin x+1\right)dx}$ using Midpoint rule.

(d)

To determine

The value of the integral ${\displaystyle \underset{e}{\overset{e+1}{\int }}\frac{1}{x\ln x}dx}$ using Midpoint rule.