CPM Homework Help : CALC Problem 6-85

What do you notice about the area under $y = \frac { 1 } { x }$ from $1$ to any positive number as it relates to the natural logarithm? Why was the area negative for part (d) above?

Hint 1:

As $x$ increases, the area increases as well. So the area function is always increasing.
But, at the beginning area increases at a greater rate than at the end.

Hint 2:

Problem 6-84 suggests that we examine the natural logarithm function, $y =\operatorname{ln}(x)$ .

Why or why not?

Use the eTool below to visualize the problem.
Click the link at right for the full version of the eTool: Calc 6-85 HW eTool