Area of the region bounded by the curve, x, +, y, = 1 and x-axis is : Option 1: 1 Option 2: 2 Option 3: 1/2 Option 4: 3/2

Answer: 1. Solution: x, +, y, =1 forms a square (rhombus) with vertices (± 1, 0), (0, ± 1). The x-axis cuts it into two triangles. Area above x-axis is a triangle with base 2 and height 1. Area = 1/2 x 2 x 1 = 1.

Calculus

Application of Integrals

Medium

common

Area of the region bounded by the curve $|x| + |y| = 1$ and x-axis is :

$\frac{1}{2}$

$\frac{3}{2}$

✅ Correct Option: 1

$|x|+|y|=1$ forms a square (rhombus) with vertices $(\pm 1, 0), (0, \pm 1)$ .

The x-axis cuts it into two triangles. Area above x-axis is a triangle with base $2$ and height $1$ .

Area $= \frac{1}{2} \times 2 \times 1 = 1$ .

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Solution

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Area of the region bounded by the curve $|x| + |y| = 1$ and x-axis is :