Question

The area bounded by $y=||x-1|-6|$ and $y=0$ is

• A. $36$ sq. units
• B. $18$ sq. units
• C. $48$ sq. units
• D. $45$ sq. units

Answer 1

The correct option is A $36$ sq. units

Curve of $y=|x|$ is


For $y=|x-1|,$ we move the curve right by $1$ units.


For $y=|x-1|-6,$ we move the curve downwards by $6$ units.


Now, graph of $y=||x-1|-6|$ is


Hence, the required area
$=\frac{1}{2}\times 12\times 6=36\text{sq.units}$