Question

The area bounded by curve $y=|x-1|$ and $y=1$ is

• A. $1$
• B. $2$
• C. $1/2$
• D. $Noneofthese$

Answer 1

The correct option is A $1$

Area $={\int }_0^2|x-1|dx$

$={\int }_0^1-(x-1)dx+{\int }_1^2(x-1)dx$

$={[x-\frac{x^2}{2}]}_0^1+{[\frac{x^2}{2}-x]}_1^2$

$=\left[\right(1-\frac{1}{2})-(0-0\left)\right]+\left[\right(\frac{2^2}{2}-2)-(\frac{1}{2}-1\left)\right]$

$=\frac{1}{2}+\frac{1}{2}$

$=1$ sq.unit (Ans)

Option A is correct.