What is the relationship between A and a in this graph?

[alingy2]

There is a graph associated to it. Please look at the screenshot.

Ok, so, here is my process.
I modeled the three functions.
y=x
y=1/a^2 x
and y=1/x

Then, I calculated A using calculus. (Integrals)
Integral of x-1/a^2 x from 0 to 1 + integral of 1/x-1/a^2 x from 1 to a
A=1-1/a^2

Now, how is a=e^A?

 

[LCKurtz]

There is a graph associated to it. Please look at the screenshot.

Ok, so, here is my process.
I modeled the three functions.
y=x
y=1/a^2 x
and y=1/x

Then, I calculated A using calculus. (Integrals)
Integral of x-1/a^2 x from 0 to 1 + integral of 1/x-1/a^2 x from 1 to a

Correct integral setups.

A=1-1/a^2

Wrong answer. Recheck your integration or show us your steps.