The curve y=∣x−2∣ is V-shaped with vertex at (2,0).
When x≥2: y=x−2
When x<2: y=2−x
To find intersection points, solve ∣x−2∣=2:
For x≥2:
x−2=2
x=4
For x<2:
2−x=2
x=0
Intersection points are (0,2) and (4,2).
The bounded region forms a triangle with:
- Vertices at (0,2), (4,2), and (2,0)
- Base = 4−0=4 units
- Height = 2−0=2 units
Area =21×base×height
Area =21×4×2
Area =4
Therefore, the area of the bounded region is 4 square units.