Find the area of the figure bounded by the curves y = |x – 1| and y = 3 - |x|.

Given;

y = |x – 1| and

y = 3 - |x|

By solving these conditions;

1 − x = 3 + x

⇒ x = −1

x − 1 = 3 − x

⇒ x = 2

Area of the region bounded by the curve y=f(x), the x-axis and the ordinates x=a and x=b, where f(x) is a continuous function defined on [a, b], is given by .

∴ Required area =

= 8 sq.units