Applications of integral calculus · manipulative

Volumes of solids of revolution

Revolve about the x-axis or the y-axis. Orbit the solid in 3D — terminals must match the axis you choose.

y = f(x) solid of revolution

Drag to orbit · scroll to zoom · sweep builds the solid from 0° to 360°

Revolve about y-axis
off = about x-axis · dx from a to b

x-terminals (a → b)

Revolution angle

360°

Volume