Find the volume of the solid obtained by rotating the region enclosed by the curves x = 1, x = 6, y = (1^4−x^4), y = 0 about the y- axis.

Answer 1

By Shell Method V = 2π∫₁⁶x(x⁴ - 1/4)dx = 2π(x⁶/6 - x²/8)₁⁶ = 2π[(6⁵ - 36/8) - (1/6 - 1/8)] = 48829.513