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Find the area of the region bounded by y – |x – 1| and y = 1.
To find are bounded by
Y = |x – 1|
y = 1
y = x – 1
or, 1 = x – 1
or, x – 2 = 0
or, x = 2
C(2,1) is point of intersection of y = x – 1 and y = 1.
y = 1 – x
1 = 1 – x
X = 0
A(0,1) is point of intersection of y = 1 – x and y = 1.
Points of intersection are A (0, 1) and C(2,1)
These are shown in the graph below: -
Required area = Region ABCA
= Region ABDA + Region BCDB
= 1 sq. units
The area of the region bounded by y = |x – 1| and y = 1 is