Integrals & FTC Lab
Undo the derivative: antiderivatives rebuild a function from its rate of change. The Fundamental Theorem of Calculus turns area problems into antiderivative evaluations — with net area keeping honest count below the axis.
1 Riemann sum lab
Watch rectangles trap the area. Choose a function and method, drag n upward, and see every Riemann sum converge to the exact FTC value.
Riemann sum = –
Exact (FTC) = –
Error = –
2 What to notice
- For an increasing function, left sums sit below the exact value and right sums above — the truth is trapped between them.
- Midpoint converges much faster than left/right: it samples each rectangle at its middle.
- The error shrinks roughly like 1/n. Doubling n halves the error — the limit is the integral.