Solids of Revolution

Enter an equation in the form shown by its field label. For example, y = sqrt(x) or x = y^2. Use sqrt(x), x^2, sin(x), arcsin(x), ln(x), pi, and e. Trigonometric angles are in radians. To select a branch, append constraints such as , x >= 0, y >= 0. A range such as , [0, inf) constrains the equation's input variable.

Enter a number or constant expression, such as sqrt(2) or pi/2. Leave either endpoint, or both, empty to calculate intersections automatically. Ambiguous regions may need an explicit bound or branch constraint.

Enter a horizontal line such as y = -1, or a vertical line such as x = 0.

Show slice controls the highlighted slice in the graph. Enable it before enabling Slice details. The text description and integral here are available independently.

On a focused graph: arrow keys orbit, Shift plus arrow keys pan, plus and minus zoom, and Home restores the view. Tab leaves the graph. On the slice preview, panning is disabled. Reset clears the revolution and slices but keeps the applied inputs.