Find the area of the region enclosed by the curve `y=|x-(1)/(x)|(xgt0)` and the line y=2

Explanation

To find the area of the region enclosed by the curve \( y = |x - \frac{1}{x}| \) for \( x > 0 \) and the line \( y = 2 \), we will follow these steps:

### Step 1: Analyze the curve
The function \( y = |x - \frac{1}{x}| \) can be split into two cases based on the value of \( x \):
- For \( 0 < x < 1 \): \( x - \frac{1}{x} < 0 \) so \( y = \frac{1}{x} - x \)
- For \( x \geq 1 \): \( x - \frac{1}{x} \geq 0 \) so \( y = x - \frac{1}{x} \)

### Step 2: Set up equations for intersections
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