Question

Using method of integration find the area bounded by the curve |x| + |y| = 1.

Answer 1

The given curve is |x| + |y| = 1
In first quadrant, (x > 0, y > 0)
Then, the line BC is x + y = 1
In third quadrant (x < 0, y <0)
Then, the line CD is -x- y =1
In fourth quadrant (x > 0, y > 0)
Then, the line DA is (x - y = 1)
Since, ABCD is a square.
$\therefore$ Required area = 4 [Area of shaded region in the first quadrant]
$=4{\int }_0^1(1-x)dx(\because x+y=1\Rightarrow y=1-x)=4[x-\frac{x^2}{2}{]}_0^1=4[(1-\frac{1}{2})-0]=2squnit$