Help please: Find the volume of the solid obtained by rotating the region bounded by the curves

Question

Find the volume of the solid obtained by rotating the region bounded by the curves:

y=x⁴, y=1

about the line y=3

Answer 1

Integration limits: x⁴ = 1; x = ±1

Volume V = π∫_-1¹[(3 - x⁴)² - 2²]dx = 2π∫₀¹(5 - 6x⁴ + x⁸)dx = 2π(5x - 6x⁵/5 + x⁹/9)₀¹ = 2π(5 - 6/5 + 1/9) = 352π/45 = 24.574