To area bounded by the lines $|x|+|y|=1$

• A

  1 sq. unit
• Correct answer
  B

  2 sq. units
• C

  $2 \sqrt{2}$ sq. units
• D

  $4 \mathrm{sq}$. units

Solution

We have, $x+y=1 \forall x, y \geq 0...(i)$ $-x+y=1 \forall x < 0, y \geq 0...(ii)$ $-x-y=1 \forall x < 0, y < 0...(iii)$ $x-y=1 \quad \forall x \geq 0, y < 0...(iv)$

Required area is the area of shaded region $\begin{aligned} &=4 \int_{0}^{1}(1-x) d x \\ &=4\left[x-\frac{x^{2}}{2}\right]_{0}^{1}=4 \times \frac{1}{2}=2 \text { sq. units } \end{aligned}$

Hence, the correct answer is option: 'B'.