Question
Using the method of integration find the area bounded by the curve |x| + |y| = 1.
[Hint: The required region is bounded by lines x + y = 1, x– y = 1, – x + y = 1 and
– x – y = 1].
Solution
The given curve is
|x| + |y| = 1
or ± x ± y = 1
The given equation represents four lines
x + y = 1, x - y = 1,
- x + y = 1 and -x - y = 1
which enclose a square of diagonal 2 units length.
Required area is symmetrical in all the four quadrants.
∴ required area = 4 (area OAB)
