What is the area enclosed in the region defined by y x ndash 1 2 line x 1 X ndash axis and Y ndash a......

What is the area enclosed in the region defined by y = |x – 1| + 2, line x = 1, X–axis and Y–axis?

The required area is essentially the area of the shaded region.
The point of intersection of y = |x – 1| + 2 where the y–axis can be found by substituting x = 0 in the equation.
Thus we get y = 3.
Required area = Area of the trapezium formed by the points (0, 0), (1, 0), (1, 2) and (0, 3).
Area of a trapezium = 1/2 * height * sum of the parallel sides
= 1/2 * 1 * (3 + 2) = 5/2 sq units
= 2.5 sq units

By: Amit Kumar