Is it possible to find the common area between curve $xy>b^2$ (rectangular hyperbola) and the rectangle $2\leq x\leq A$ and $2\leq y\leq B$ where $A$ and $B$ are much larger than $b^2$?
From what I think, it should be something like area of rectangle subtracted the area of hyperbola with x-axis. But doing this we also remove the area that is not in the rectangle(for some values of $b^2$), so we add that small part again.
However, how to calculate the area between the hyperbola and x-axis. If I integrate the hyperbola from $2\leq x\leq A$ what about the bound on $y$, how to consider both the bounds?
I don't know if it's really the right approach, but it should not be undefined because $x$ and $y$ are bounded. So how do I calculate the area?