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]dot`

Explanation

To find the area bounded by the curve \( |x| + |y| = 1 \), we can start by understanding the shape of the region defined by this equation. The equation describes a diamond (or rhombus) centered at the origin with vertices at the points (1, 0), (0, 1), (-1, 0), and (0, -1).

### Step-by-Step Solution:

1. **Identify the Lines**: The equation \( |x| + |y| = 1 \) can be rewritten in terms of four linear equations based on the signs of \( x \) and \( y \):
- \( x + y = 1 \) (1st quadrant)
- \( x - y = 1 \) (4th quadrant)
- \( -x + y = 1 \) (2nd quadrant)
...