Chapter 16.4, Problem 39E

(a)

To determine

To approximate: The definite integral ${\displaystyle \underset{1}{\overset{b}{\int }}f\left(x\right)}dx$ using calculator for $b=20,50,100,1000\text{and}10,000$.

(b)

To determine

Whether the integral ${\displaystyle \underset{1}{\overset{\infty }{\int }}f\left(x\right)}dx$ based on part (a) is convergent or divergent.

(c)

To determine

To approximate: The definite integral ${\displaystyle \underset{1}{\overset{b}{\int }}g\left(x\right)}dx$ through graphing calculator for $b=20,50,100,1000\text{and }10,000$.

(d)

To determine

Whether the integral ${\displaystyle \underset{1}{\overset{\infty }{\int }}g\left(x\right)}dx$ based on the results of part (c) is convergent or divergent.

(e)

To determine

To explain: How the results of part (b) and part (d) can be guess by comparing the integrals with others whose convergence/divergenceis known.