Calc II Explorer

Calculus II — Geometry & Applications

Interactive companions for a second-semester calculus course. Enter your own functions, move a slider, and watch the picture behind the integral: the region, the slice, the solid it sweeps out, and the thin piece whose work adds up.

Volumes

Volumes of Revolution Live

Revolve a region about any horizontal or vertical axis. Disk/washer or shell method, an animated sweep of the revolution, and the moving cross-section in 3D.

Volumes by Cross-Sections Live

Stand squares, circles, semicircles or right triangles on a base region and watch the solid build up slice by slice, with the moving cross-section in 3D.

Work

Work: Lifting a Load Live

Winch a crate, a leaking sandbag or a rolled poster to the roof on a cable that weighs something itself, and watch the force split into its load and cable parts.

Work: Stretching a Spring Live

Stretch or squeeze a spring against Hooke's law, and see why a force that grows with the stretch makes the work an area rather than a product.

Work: Pumping a Tank Live

Empty a box, cylinder, cone, lying cylinder or ball one thin layer at a time, and build the integral a step at a time with the answers folded away.

Practice

u-Substitution Match Live

A sixty-second game: link each integral to its substitution, to the differential that forces, and to the integral it becomes. Match the whole chain to clear it.

Planned

Sequences & Series Coming soon

Partial sums marching toward a limit, with the comparison, ratio and integral tests made visual.

Power Series & Taylor Coming soon

Taylor polynomials tightening around a function, with the interval of convergence drawn in.

Parametric & Polar Curves Coming soon

Trace a curve as the parameter runs, and sweep out area in polar coordinates.