Chapter 4.6, Problem 1ES

(a)

To determine

To compute: The Simpson’s rule approximation $S\left(a,b\right),S\left(a,\frac{a+b}{2}\right)\text{ and }S\left(\frac{a+b}{2},b\right)$ for the integral ${\displaystyle \underset{1}{\overset{1.5}{\int }}{x}^2\ln x}dx$.

(b)

To determine

To compute: The Simpson’s rule approximation $S\left(a,b\right),S\left(a,\frac{a+b}{2}\right)\text{ and }S\left(\frac{a+b}{2},b\right)$ for the integral ${\displaystyle \underset{0}{\overset{1}{\int }}{x}^2{e}^{-x}}dx$.

(c)

To determine

To compute: The Simpson’s rule approximation $S\left(a,b\right),S\left(a,\frac{a+b}{2}\right)\text{ and }S\left(\frac{a+b}{2},b\right)$ for the integral ${\displaystyle \underset{0}{\overset{0.35}{\int }}\frac{2}{x^2-4}}dx$.

(d)

To determine

To compute: The Simpson’s rule approximation $S\left(a,b\right),S\left(a,\frac{a+b}{2}\right)\text{ and }S\left(\frac{a+b}{2},b\right)$ for the integral ${\displaystyle \underset{0}{\overset{\frac{\pi }{4}}{\int }}{x}^2\sin x}dx$.