The area bounded by the curves y = |x| - 1 an | vedclass

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

Vedclass · Accepted Answer

$2$

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(B) The given curves are $y = |x| - 1$ and $y = -|x| + 1$.These curves represent a square with vertices at $(1, 0), (0, 1), (-1, 0),$ and $(0, -1)$.Alternatively,we can analyze the regions:For $x \ge 0$,the curves are $y = x - 1$ and $y = -x + 1$.For $x The region is symmetric about both axes.The area in the first quadrant is bounded by $y = x - 1$ (for $x \ge 1$,but here the intersection is at $x=1, y=0$) and $y = -x + 1$.Actually,the region is a square formed by the lines $y = x - 1, y = -x - 1, y = -x + 1,$ and $y = x + 1$.The area of this square is $4 	imes (	ext{Area of triangle in one quadrant})$.Each triangle in a quadrant has base $1$ and height $1$.Area $= 4 	imes (\frac{1}{2} 	imes 1 	imes 1) = 2$ square units.

The area bounded by the curves $y = |x| - 1$ and $y = -|x| + 1$ is

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