Question

use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. y=x^(1/3), y=0, x=1

Answer 1

y = x^(1/3)
y^3 = x
y^6 = x^2

Vol = π∫(1^2 - x^2) dy from 0 to 1
= π [ y - y^7 /7] from 0 to 1
= π(1 - 1/7 - 0)
= 6π/7