Hello, asnxbbyx113!
This can be done with cylindrical shells, too.
Find the volume of the solid obtained by rotating the region bounded by:
. . y = 2x², 0 < x < 2, y = 8; about the y-axis. . V . = . 2π ∫ x·y dxCode:| 8+ - - - - * |::::::::: |::::::::* |::::::* |:::* ----*----------+--- | 2
. . . . . . . . . . . . . . . 2
We have: .V .= .2π ∫ x(8 - 2x²) dx . = . 16π
. . . . . . . . . . . . . . 0