Question

The area of the region bounded by the curve $ y = \max\{|x|, |x-2|\} $, then x-axis and the lines x = -2 and x = 4 is equal to ____.

Hint:

The solution provided in the picture calculates the area as a sum of triangular areas.

Answer 1

Correct Answer: 12

The area calculation, as depicted in the image, is as follows:

Required Area = \( \frac{1}{2} \times 2 \times 2 + \frac{1}{2} \times 3 \times 3 + \frac{1}{2} \times 1 \times 11 \)
Required Area = \( 2 + \frac{9}{2} + \frac{11}{2} \)
Required Area = \( 2 + \frac{20}{2} \)
Required Area = \( 2 + 10 \)
Required Area = \( 12 \)
Therefore, based on the provided solution, the calculated area is 12.