Chapter 11.6B, Problem 5GCE

To determine

To find the areas of the regions under the graph of $y=\frac{1}{x}$ and how do the values compare with $\ln 0.6,\ln 0.5$ , and $\ln 0.4$ .

Explanation of Solution

Given:

Use $x=1$ as the lower limit and $x=0.6,0.5$ , and $0.4$ as upper limits.

Calculation:

Area under curve $y=\frac{1}{x}$ on interval $[1,0.6]$ is $0.50182$ square unit.

Area under curve $y=\frac{1}{x}$ on interval $[1,0.5]$ is $0.69314$ square unit.

Area under curve $y=\frac{1}{x}$ on interval $[1,0.4]$ is $0.9162$ square unit.

These all values are equal to the absolute values of $\ln 0.6,\ln 0.5$ , and $\ln 0.4$ .