Find the area enclosed by the curves y = |x – 1| and y = – |x – 1| + 1.

To find the area enclosed by

y = |x – 1|

And y = – |x – 1| + 1

Solving both the equation for x<1

Y = 1 – x and y = x,

We get x = and y =

And solving both the equations for x≥1

Y = x – 1 and y = 2 – x,

We get x = and y =

These are shown in the graph below:

Required area = Region ABCDA

Required area = Region BDCB + Region ABDA …(1)

The area enclosed by the curves y = |x – 1| and y = – |x – 1| + 1 is

46