Source: Extra Practice
Find the area bounded by the parabola x² = 4y and the line y = 4.
Options
Option A
32/3 sq. units
Option B is correct
64/3 sq. units
Option C
16/3 sq. units
Option D
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.