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].`

Explanation

Given curve, `|x| +|y|=1`

In first quadrant (x gt 0, y gt 0) then line AB is
`x+y=1.`
In second quadrant (x lt 0, y gt 0) then line BC is
`-x+y=1.`
In third quadrant (x lt 0, y lt 0) then line CD is
`-x-y=1.`
In fourth quadrant (x gt 0, y lt 0) then line DA is
`x-y=1`.
Since ABCD is a square
therefore, required area = 4 `xx` (area of shaded region in first quadrant)
`=4int_(0)^(1)(1-x)dx`
`=4[x-(x^(2))/(2)]_(0)^(1)=4[(1-(1)/(2))-0]`
`=2` sq. units.