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What is the area enclosed by the curves y = 2 − |2 − x| and y = 3/|x|?

1. (5 − 4 ln 2)/3 square units
2. (2 − ln 3)/2 square units
3. (4 − 3 ln 3)/2 square units
4. None of these

Correct answer: (4 − 3 ln 3)/2 square units

Solution

The area enclosed by the curves y = 2 − |2 − x| and y = 3/|x| is (4 − 3 ln 3)/2 square units because it is calculated by integrating the difference between the two functions over the relevant interval.

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