find the volume of the solid

Question

Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=x² and y=4 about the line y=4. 

volume=?

Answer 1

x² = 4; x = ±2. Volume v = π∫_-2²(4 - x²)²dx = 2π∫₀²(16 - 8x² + x⁴)dx = 2π(16x - 8x³/3 + x⁵/5)₀² = 2π(32 - 64/3 + 32/5) = 512π/15