Question

Let $f\left(x\right)=\text{minimum}\{|x-1|,|x|,|x+1|\}$, then the area bounded by $f\left(x\right),x=\pm 1$ and $y=0$, in sq. units, is:

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $\frac{1}{3}$
• D. $\frac{1}{6}$

Answer 1

The correct option is A $\frac{1}{2}$

As shown in the figure, we have to calculate area of the shaded region.
Area $=2\times \frac{1}{2}\times 1\times \frac{1}{2}$
Area $=\frac{1}{2}$