Find the area enclosed by the equations:
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:
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:
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?