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The region enclosed between y = a/(4 + x²) (with a > 0) and the line y = c (with c <= 0) has an area equal to the only even prime number. Find [a] + [c], where [.] is the greatest integer function.

1. 1
2. 0
3. -1
4. 3

Correct answer: 1

Solution

Since the curve is positive and c <= 0, the only finite enclosed area uses c = 0, giving area (a*pi)/2 = 2, so a = 4/pi (about 1.27); then [a] = 1 and [c] = 0, summing to 1.

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