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What do you notice about the area under from to any positive number as it relates to the natural logarithm? Why was the area negative for part (d) of 6-86?  

As 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, .

Is this graph a good model of the growth in area of ?

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