Let R be the region enclosed by x=2, x=3, y=16-x^4 and y =0. Find the volume of the solid obtained by rotating R around the y-axis.

Answer 1

By Shells Method V = 2π∫₂³x(x⁴- 16)dx = 2π(x⁶/6 - 8x²)₂³ = 2π[(243/2 - 72) - (32/3 - 32)] = 425/3π