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The curve y = a*sqrt(x) + b*x passes through (1, 2) and lies above the x-axis for 0 <= x <= 9. If the area enclosed by the curve, the x-axis and the lines x = 0 and x = 4 is 8 square units, which of the following is correct?

1. a = 1
2. b = 1
3. a = 3
4. b = -1

Correct answer: a = 3

Solution

From a + b = 2 and (16a/3) + 8b = 8, solving gives a = 3 and b = -1, so a = 3 is correct.

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