This is multi-part problem, starting with:

Consider the region in the first quadrant that is bounded above by

, and below by

. A is the unknown parameter, which allows the above to be true, and should be considered a constant.

We are to write a definite integral for this, leaving the final answer in terms of A.

So, when graphing this, you can see that

only goes from 0 to 1. I figured that this would mean that our definite integral would go from 0 to 1, but apparently this is wrong. The integral I got was

but, I guess the bounds should be from 0 to some number, say z. I understand that the bounds of integration are dependent on A, but I'm not sure how, exactly.

Any help would be great, I've been wracking my brain for a couple days on this problem.