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

As given in the picture, the area is calculated as:

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 = \( 12 \) 
Thus, following the given solution, the area is 12.