Finding the area between two regions in the plane

Question

I have two regions, given by $y>\sqrt{2}x - \frac{1}{4x}$ and $y< \sqrt{2}x + \frac{1}{4x}$. How can I find the area of their intersection? If their is no easy analytical way, could someone perhaps use a computer? I am not sure how.

Answer 1

We can notice that the searched area is:

$$\int_0^{\infty} \sqrt{2}x+\frac{1}{4x}-(\sqrt{2}x-\frac{1}{4x})=\frac{1}{2}\int_0^{\infty}\frac{1}{x}=\infty$$

:)