Question

Find the volume of the solid formed by revolving the region bounded by y=x^3, x=2 and y=1 about the y-axis.

Please help =(

Answer 1

Did you make a sketch?

I would calculate the volume of a cylinder with radius 2 and height of 1, then subtract the region bounded by the y-axis, y= x^3 and y = 1

that volume is
[integral] (πx^2)dy from 0 to 1
= π[integral] y^(2/3) dy from 0 to 1
= π ((3/5)y^(5/3) | from 0 to 1
= π(3/5 - 0) = 3π/5

So volume = π(2)^2(1) - 3π/5 = 4π - 3π/5 = 17π/5

check my arithmetic