Question

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

Answer 1

To find the area enclosed by

y = |x – 1|

Solving both the equation for x < 1

Y = 1 – x and y = x,

We get x = \(\frac{1}{2}\) and y = \(\frac{1}{2}\)

And solving both the equations for x ≥ 1

Y = x – 1 and y = 2 – x,

We get x = \(\frac{3}{2}\) and y = \(\frac{1}{2}\)

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 \(\frac{1}{2}\) sq. units.