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Find the area bounded by the parabola y² = 4*a*x, its axis (the x-axis), and the two ordinates x = 4 and x = 9.

1. 4a²
2. 16*sqrt(a)/3
3. 76*sqrt(a)/3
4. 152*sqrt(a)/3

Correct answer: 152*sqrt(a)/3

Solution

Integrating the upper half of the parabola between x = 4 and x = 9 gives (4/3)*sqrt(a)*(9^(3/2) - 4^(3/2)) = 152*sqrt(a)/3.

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