The area bounded by the curve y = ||x-1|-2| and the x-axis is ________.

Question

The area bounded by the curve $y = \bigl||x-1|-2\bigr|$ and the $x$-axis is \_\_\_\_\_\_\_\_.

Answer: 4

Accepted Answer

The graph forms a triangle $PQR$ dipping below the axis before folding up, with base $PR=4$ and height $AQ=2$ (peak of the reflected dip).

$$\text{Area} = \frac12\times\text{Base}\times\text{Height} = \frac12\times4\times2 = 4$$

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