Explanation

(b)
Since, $|x| + |y| = 1$
$\Rightarrow \ \left\{ \begin{array}{r}
x + y = 1,\ x > 0,\ y > 0 \\
x - y = 1,\ x > 0,\ y < 0 \\
- x + y = 1,\ x < 0,\ y > 0 \\
- x - y = 1,\ x < 0,\ y < 0
\end{array} \right.\$
and $1 - y^{2} = |x|$
[image:8_image80.png]
$\Rightarrow \ \left\{ \begin{array}{r}
1 - y^{2} = x,\ x \geq 0 \\
1 - y^{2} = - x,\ x < 0
\end{array} \right.\$
$\therefore$ Required area $= \left| 2\int_{0}^{1}{\sqrt{(1 - x)}dx} \right| + \left| 2\int_{- 1}^{0}{\sqrt{(x + 1)}dx} \right| - 4\left( \frac{1}{2} \bullet 1 \bullet 1 \right)$
$= \frac{2}{3}\ sq\ unit$