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If the area enclosed between the x-axis and the curve y = 6x - 3x² from x = 1 to x = a equals 19 square units, then the value of 'a' can lie in which range?

1. a = 4 or a = -2
2. two values lie in (2, 3) and one in (-1, 0)
3. two values, one in (3, 4) and one in (-2, -1)
4. none of these

Correct answer: two values, one in (3, 4) and one in (-2, -1)

Solution

Solving the area-equals-19 condition gives two admissible values of a, one located in (3,4) and one in (-2,-1).

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