Question

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

[Hint: The required is bounded by lines x + y = 1, – x + y = 1 and - x -y = 1].

Answer 1

|x|+ |y| = 1

so points are (0, 1) (0, -1) (1, 0) (-1, 0)

but |x| + |y| = 1 can be written as: follows:

⇒ -x + y = 1 (2nd quadrant); x + y =1

(1st quadrant); x – y = 1 (4th quadrant); -x -y = 1 (3rd quadrant) .

|x|+ |y| = 1 in different quadrants

Not by Integration

so area required (shaded)

= 4 x Area of any one part Δ

= 4 x Area Δ ABC

By integration

Area required

= 4 x Area of ΔABC

= 4 x Area under line AC (x + y = 1)