Find the volume of solid generated if the area bounded by each of the following curves is revolved about the indicated axis/line.

Question

y = x³ + 1 , then axis, x = 3, OX

Answer 1

Let get x intercept of y = x³ + 1 = 0, from here x = (- 1)^1/3 = - 1. Because using Disk method for volume we have: V = π∫_-1³(x³ + 1)²dx = π ∫_-1³(x⁶ + 2x³ + 1)dx = π(x⁷/7 + x⁴/2 + x)_-1³ = π[(3⁷/7 + 3⁴/2 + 3) - ( - 1/7 + 1/2 - 1)] = 2496π/7