The area bounded by the curves |x| + |y| geq | vedclass

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Question

(C) The region $|x| + |y| \leq 1$ represents a square with vertices at $(1, 0), (0, 1), (-1, 0), (0, -1)$.The region $x^2 + y^2 \leq 1$ represents a c

Vedclass · Accepted Answer

$(\pi - 2) 	ext{ sq. units}$

Vedclass · Answer

(C) The region $|x| + |y| \leq 1$ represents a square with vertices at $(1, 0), (0, 1), (-1, 0), (0, -1)$.The region $x^2 + y^2 \leq 1$ represents a circle with radius $r = 1$ centered at the origin.The area of the circle is $A_c = \pi r^2 = \pi(1)^2 = \pi$.The area of the square $|x| + |y| \leq 1$ is $A_s = \frac{1}{2} 	imes d_1 	imes d_2 = \frac{1}{2} 	imes 2 	imes 2 = 2$.Since the square is inscribed within the circle,the area bounded by the curves $x^2 + y^2 \leq 1$ and $|x| + |y| \geq 1$ is the area of the circle minus the area of the square.Required Area $= A_c - A_s = \pi - 2 	ext{ sq. units}$.

The area bounded by the curves $|x| + |y| \geq 1$ and $x^2 + y^2 \leq 1$ is

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