The area bounded by the curve, -x, +, -y, =2 is Option 1: 2 sq. units Option 2: 4 sq. units Option 3: 6 sq. units Option 4: 8 sq. units

Answer: 8 sq. units. Solution: Since, -x, =, x, and, -y, =, y, the curve is, x, +, y, =2, a square with vertices (± 2,0) and (0,± 2). Both diagonals are 4, so the area is 1/2x 4x 4=8 square units.

Calculus

Application of Integrals

Easy

common

The area bounded by the curve $|-x|+|-y|=2$ is

2 sq. units

4 sq. units

6 sq. units

8 sq. units

✅ Correct Option: 4

Since $|-x|=|x|$ and $|-y|=|y|$ , the curve is $|x|+|y|=2$ , a square with vertices $(\pm 2,0)$ and $(0,\pm 2)$ . Both diagonals are 4, so the area is $\frac{1}{2}\times 4\times 4=8$ square units.

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The area bounded by the curve $|-x|+|-y|=2$ is