Calculus
Line integrals: compare two paths
Follow two paths and build sums one contribution at a time. Compare work, length and mass against exact values, distinguishing path dependence from numerical error.
The paths have different endpoints: this is not a test of path dependence with fixed endpoints.
Curves, field and current contribution
Blue: A; orange: B; purple: current element. Field arrows share one scale in the view. No force field is shown for scalar integrals.
Partial sums along parameter t
Path A
Current step with the numbers
Path B
Current step with the numbers
The final comparison
Value table
What changes as n increases
Midpoint sums, not a universal symbolic solver. The corner is split exactly even with t². Actual cell count may exceed n by one. Errors compare with exact preset formulas, not certified bounds. Animation advances by cells, not physical motion time.