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#### Pranav

##### Well-known member

- Nov 4, 2013

- 428

**Problem:**

Calculate the area of region defined by the inequalities:

$$-1<xy<1$$

$$-1<x^2-y^2<1$$

**Attempt:**

Although I have solved the problem but I am not very satisfied with the method I used. The graph of region is symmetrical in all the four quadrants so I calculated the area in the first quadrant and multiplied by 4. I found the points of intersection and got the following integrals:

Wolfram Alpha

But I feel that given the shape of region, there exists an easier method. Has someone got any idea about a shorter method?

Here's an image depicting the region:

Any help is appreciated. Thanks!