Question

Using the method of integration, find the area bounded by the curve $\left|x\right|+\left|y\right|=1$ .

Answer 1

Graph of the equation $\left|x\right|+\left|y\right|=1\{\begin{array}{c}x+y=1\\ x-y=1\\ -x+y=1\\ -x-y=1\end{array}$

Required area $=4{\int }_0^1(1-x)dx$
$=4{[x-\frac{x^2}{2}]}_0^1$
$=2\text{sq.units}$