The area of the region $A = \{(x, y) : 0 \leq y \leq |x| + 1 ext{ and } -1 \leq x \leq 1\}$ in sq. units, is

Question

The area of the region $A = \{(x, y) : 0 \leq y \leq |x| + 1 	ext{ and } -1 \leq x \leq 1\}$ in sq. units, is

Aicharya · Accepted Answer

x x = x 2 , &#160; x &#8805; 0 - x 2 , &#160; x &#60; 0 Area enclosed = &#8747; - 1 0 - x 2 + 1 d x + &#8747; 0 1 x 2 + 1 d x = - x 3 3 + x - 1 0 + x 3 3 + x 0 1 = 2

The area of the region $A = \{(x, y) : 0 \leq y \leq |x| + 1 \text{ and } -1 \leq x \leq 1\}$ in sq. units, is

Solution