Chapter 15.3, Problem 21E

(a)

To determine

To fill: The list on the calculator with value of $x^2$ as x approaches from 0.1 to 1 using the command $Seq\left(x^2\right)$.

(b)

To determine

To find: The value using the command $\left(0.1\right)\text{sum}\left({\text{L}}_1\right)$ listed in part (a) to estimate ${\displaystyle {\int }_0^1{x}^2}dx$.

(c)

To determine

To find: The list of $Seq\left(x^2\right)$ and the value of $\text{sum}\left({\text{L}}_1\right)$ for the listed $Seq\left(x^2\right)$ when $n=100$ and estimate ${\displaystyle {\int }_0^1{x}^2}dx$.

(d)

To determine

To find: The list of $Seq\left(x^2\right)$ and the value of $\left(0.002\right)\text{sum}\left({\text{L}}_1\right)$ for the listed $Seq\left(x^2\right)$ when $n=500$ and estimate ${\displaystyle {\int }_0^1{x}^2}dx$.

(e)

To determine

To estimate: The value of ${\displaystyle {\int }_0^1{x}^2}dx$ through part (b) to part (d).