Find the area bounded by the parabola x² = 4y and the line y = 4.

Model Answer & Options

Source: Extra Practice

32/3 sq. units

64/3 sq. units

16/3 sq. units

128/3 sq. units

Explanation

The curve is symmetric about the y-axis. The intersection points are x² = 4(4) = 16, so x = -4 and x = 4. Area = ∫[-4 to 4] (4 - x²/4) dx = 2 * ∫[0 to 4] (4 - x²/4) dx = 2 * [4x - x³/12] from 0 to 4 = 2 * [16 - 64/12] = 2 * [16 - 16/3] = 2 * [32/3] = 64/3. Option A is only half the area (one side). Options C and D are arithmetic mistakes.

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