Surface area of a line rotated about x axis

Question

Can u guys find the surface area of y=(x^3)/3 rotated about x axis (0=<x=<1)

Answer 1

Surface area S = 2π∫₀¹f(x)√1 +f'²(x)dx = 2π∫₀¹(x³/3)(1 + x⁴)^1/2dx = 2π/3·1/4(1 + x⁴)^3/2·2/3₀¹ = π

π/9[2^3/2 - 1) = π(2√2 - 1)/9 = 0.638