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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) above? 

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 6-84 suggests that we examine the natural logarithm function, .

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