I want to calculate the area of a compact subset $B \subset \mathbb{R}^2$ whose area is confined by the curves $$xy = 4 \wedge x=y \wedge x = 4$$
I've tried to just go the where naive route of integrating the difference of the "upper" function and the "lower" funtion like this:
$$V(B) = \int_2^4 x - \frac{4}{x} dx$$
Since the other tasks on the sheet are pretty difficult measure theory tasks I find it difficult to believe that this calculation is actually correct because it's way too easy. Can anyone confirm or deny that this is indeed the correct value? Thanks in advance!
Just a small typo of $dy$ shouldn't be there.
The expression of $V(B)=\int_2^4 x - \frac4x \, dx$ is correct.