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

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(B) Step $1$: Identify the curves. The curve $y = |x| - 1$ represents a $V$-shape with vertex at $(0, -1)$. The curve $y = -|x| + 1$ represents an inv

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$2$ sq. units

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(B) Step $1$: Identify the curves. The curve $y = |x| - 1$ represents a $V$-shape with vertex at $(0, -1)$. The curve $y = -|x| + 1$ represents an inverted $V$-shape with vertex at $(0, 1)$.Step $2$: Find the intersection points. Setting $|x| - 1 = -|x| + 1$, we get $2|x| = 2$, so $|x| = 1$, which means $x = 1$ or $x = -1$. At $x = 1$, $y = 0$. At $x = -1$, $y = 0$. The intersection points are $(1, 0)$ and $(-1, 0)$.Step $3$: The bounded region is a square (or rhombus) with vertices at $(0, 1), (1, 0), (0, -1),$ and $(-1, 0)$.Step $4$: The area of a rhombus with diagonals $d_1$ and $d_2$ is $\frac{1}{2} 	imes d_1 	imes d_2$. Here, $d_1$ (vertical) $= 1 - (-1) = 2$ and $d_2$ (horizontal) $= 1 - (-1) = 2$.Step $5$: Area $= \frac{1}{2} 	imes 2 	imes 2 = 2$ sq. units.

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

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