Question

Using the method of integration find the area bounded by the curve\(|x|+|y|=1\)
[Hint:the required region is bounded by lines \(x+y=1,x–y=1,–x+y=1\) and \(–x–y=11\)]

Answer 1

The correct answer is:\(=2units\)
The area bounded by the curve,\(|x|+|y|=1\), is represented by the shaded region ADCB
as

The curve intersects the axes at points A(0,1),B(1,0),C(0,–1),and D(–1,0).
It can be observed that the given curve is symmetrical about \(x-axis\) and \(y-axis.\)
\(∴Area\,\, ADCB=4\times Area\,\, OBAO\)
\(=∫^1_0(1-x)dx\)
\(=4\bigg(x-\frac{x^2}{2}\bigg)^1_0\)
=\(=4[1-\frac{1}{2}]\)
\(=4(\frac{1}{2})\)
\(=2units\)