Chapter 5.4, Problem 62E

(a).

To determine

To Find: The value of $b\text{for}\left(b>0\right)$ such that the region bounded by the cubic $y=\frac{1}{x}\left(\text{for}x\ge 1\right)$ and the x-axis on the interval $\left[1,b\right]$ has area 1.

(b).

To determine

To Find: The value of $b\text{for}\left(b>0\right)$ such that the region bounded by the cubic $y=\frac{1}{x^p}$,where $x\ge 1$ ,and $p<2$ with $p\ne 1$ and the x-axis on the interval $\left[1,b\right]$ has area 1.

(c).

To determine

To show: The function $b\left(b\right)={\left(2-p\right)}^{\frac{1}{1-p}}$ is an increasing or decreasing function of $p$.