Plot a function and shade the area under it

Plot $f(x)$ and layer on calculus visuals.

Set the expression

1. Add a function_graph object (or pick one of the classic-function presets in its Geometry tab).
2. Edit f(x) = using numpy syntax, e.g. np.sin(x), x**2 - 1, np.exp(-x**2).
3. Set Axes to attach the graph to an axes object already in the scene — the graph is plotted in that axes' coordinate space.
4. Set the plotted domain (X− / X+).

Shade the area under the curve

Toggle Area under curve (showArea), then set From/To (areaFrom/areaTo) to bound the shaded region:

$$\int_a^b f(x)\,dx$$

Riemann rectangles

Toggle Riemann rectangles (showRiemann) for approximation rectangles over the same From/To region, and set Δx (riemannDx) for the rectangle width — smaller Δx means more, thinner rectangles approximating the integral more closely.

Area and Riemann rectangles share the same From/To bounds, so you can toggle between them (or show both) without re-entering the interval.

Tangent line

Toggle Tangent line (showTangent), then set at x (tangentX) for where it touches the curve. tangentX is keyframeable — animate it with record mode or a ◆ diamond to slide the tangent line along the curve as the scene plays.

Tracked point

Toggle Tracked point (showTracker), then set at x (trackerX) for where the dot sits on the curve — needs Axes attached, since the dot's position is computed via that axes' coordinate system. Like tangentX, trackerX is keyframeable: animate it to sweep the dot along the curve for the classic "watch the point trace the function" or "watch a limit approach" moment. Turn on Show (x, f(x)) label to display the dot's live coordinates next to it.

Derivative curve

Toggle Derivative curve f′(x) (dashed) (showDerivative) to plot $f'(x)$ alongside $f(x)$ as a dashed curve.

Numeric readouts

Under Graph Analyzer, each of these is computed numerically from $f(x)$ and prints a live readout on the canvas:

See Animation reference for how tangentX and the other numeric fields behave once keyframed.