### Home > APCALC > Chapter 6 > Lesson 6.3.1 > Problem6-88

6-88.

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) of 6-86?

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.

Problem 6-86 suggests that we examine the natural logarithm function, $y = \ln(x)$.

Is this graph a good model of the growth in area of $y=\frac{1}{x}$?

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 6-88 HW eTool