Integrals & FTC Calculator
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 FTC evaluator + Riemann sums
Enter a polynomial f(x) = a₀ + a₁x + a₂x² + a₃x³ and bounds a, b. Get the antiderivative, the exact FTC value, and Riemann sums that converge to it.
Steps
Enter values and press Evaluate.
2 Why it works
- The antiderivative reverses differentiation term by term (power rule).
- The FTC says the definite integral equals F(upper) − F(lower) — net area, sign and all.
- Riemann sums (left, right, midpoint, trapezoid) approximate the same number; they converge as n grows.