Question

The area bounded by curves y = |x| – 1 and y = – |x| + 1 is

• A. 1
• B. 2
• C. 2 $\sqrt { 2 }$
• D. 4

Answer 1

Answer: (B)

2

Answer 2

y = |x| – 1 ̃ $\left\{ \begin{array} { l l } \mathrm { y } = - \mathrm { x } - 1 , & \mathrm { x } < 0 \\ \mathrm { y } = \mathrm { x } - 1 , & \mathrm { x } > 0 \end{array} \right.$

y = – |x| + 1 ̃

\ x + y = – 1, x – y = – 1, when x < 0 x – y = 1, x + y = `1, when x > 0

Obviously all these four lines form square ABCD whose side =$\sqrt { 2 }$. Hence required
area = area of the square = 2