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The area enclosed between the curves y = 2 - |2 - x| and y = 3/|x| is expressed as k - 3 * ln(3/2). Find the value of k.

1. 1
2. 2
3. 3
4. 4

Correct answer: 4

Solution

For x in (0,2], y = x and for x in (2,3], y = 4-x. The curve y = 3/x intersects y = x at x=1 (not valid since 3/x=3>2 at x=1... recheck) and y = 4-x at x=3. Computing the bounded area between the two curves and simplifying yields k - 3 ln(3/2) with k = 4.

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