Area bounded by the curves y = |x| - 1 and y | vedclass

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Question

(A) The given curves are $y = |x| - 1$ and $y = 1 - |x|$.These curves represent a square with vertices at $(1, 0)$,$(0, 1)$,$(-1, 0)$,and $(0, -1)$.Th

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) The given curves are $y = |x| - 1$ and $y = 1 - |x|$.These curves represent a square with vertices at $(1, 0)$,$(0, 1)$,$(-1, 0)$,and $(0, -1)$.The side length of this square can be calculated using the distance formula between two adjacent vertices,for example,$(1, 0)$ and $(0, 1)$:$s = \sqrt{(1-0)^2 + (0-1)^2} = \sqrt{1^2 + (-1)^2} = \sqrt{1+1} = \sqrt{2}$.The area of a square is given by $s^2$.Therefore,the area is $(\sqrt{2})^2 = 2$ square units.

Area bounded by the curves $y = |x| - 1$ and $y = -|x| + 1$ is (in square units)

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