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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