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## Homework Statement

Find the area enclosed by the equations:

[itex]y=1/x[/itex]

and

[itex]y=1/x^2[/itex]

and

[itex]x=2[/itex]

## Homework Equations

N/A

## The Attempt at a Solution

So I solved this analytically after looking at a graph of the two functions. Using integrals I got the following:

[itex]ln(2)-1/2[/itex]

Which is the correct answer. I assumed the bounds of the integral were 0 as well as 2, due to the fact that I thought I'd get infinite area if I used the whole negative x-axis for a bound. My issue is that when I was solving analytically I got:

[itex]-ln(0)-1/0[/itex]

as the lower bound value I was subtracting from the upper bound of the integral. And while I just wrote it off as something I can omit from my answer (and got the right answer anyway), I can't help but feel I'm missing something conceptually from this problem. For instance, It seemed to me at first like [itex]y=1/x^2[/itex] should have been the top function and I should subtract the area of [itex]y=1/x[/itex]. But that is apparently not the case. And I'm also not sure how I can reasonably pick 0 as the lower bound of the integral when it's undefined in the answer I got.

So where is my understanding failing me?

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