Question

The area bounded by the curves \(y = |x|-1\) and \(y = -|x|+1\) is

• A. \(1\) sq.unit
• B. \(2\) sq. units
• C. \(2\sqrt{2}\) sq.units
• D. \(4\) sq.units

Hint:

The two V-shaped graphs form a square; integrate the gap between them.

Answer 1

The Correct Option is B

Step 1: Find the vertices:
The two graphs cross the x-axis at $(\pm1, 0)$ and meet the y-axis at $(0, 1)$ and $(0, -1)$. The enclosed shape has these four corners.

Step 2: Shape:
All four sides have length $\sqrt2$ and the diagonals are equal (length 2), so it is a square.

Step 3: Area:
Side squared is $(\sqrt2)^2 = 2$.

Final Answer:
The area is 2 square units, option (B). \[ \boxed{2\text{ sq. units}} \]