Find the area of curve enclosed by : `|x+y|+|x-y|le4,|x|le1,y gesqrt(x^(2)-2x+1)`.

Answer

2 sq. units

Explanation

`R_(1): |x+y|+|x-y|le4`
Considering `x+y+x-y le 4," we get "xle2`
Similarly, for other cases, we get `ge-2, yle2 and yge -2`
`therefore" "R_(1)" is the square bounded by lines "x=pm2 and y=pm 2`
`R_(2) : |x|le1`
`therefore" "-1lexle1`
`therefore" "R_(2)" is the region of all points between "x=pm 1`
`ygesqrt(x^(2)-2x+1)`
`R_(3) : y ge |x-1|`
`therefore" "R_(3)" is the open triangular region above x-axis between the lines "y=1-x and y=x-1`
`therefore" "` Required common region is as shown in the following figure.

Required Area = Area of the shaded portion
`=(1)/(2)xx2xx2` sq. units = 2 sq. units