Is this geometric area?
It is signed (net) area unless the curve stays non-negative.
Area Under the Curve Calculator
Integrate a power function or quadratic on [A, B] to get net signed area.
Enter the function and limits
Choose power or quadratic mode, enter coefficients, then limits A and B.
About this calculator
How to use Area Under the Curve Calculator, plus the formulas and logic behind the results.
Tool description
The definite integral equals net signed area between the curve and the x-axis from A to B.
How to use
- Select power or quadratic mode.
- Enter coefficients and the limits A, B.
- Select Calculate to view the definite integral.
- Take absolute values on subintervals if you need geometric area only.
Formulas & reference
∫_A^B a xⁿ dx = a/(n+1)[Bⁿ⁺¹ − Aⁿ⁺¹] (n ≠ −1)∫_A^B (ax²+bx+c) dx = [a x³/3 + b x²/2 + c x]_A^B
Area tips
- Split at roots if you need total geometric area
- n = −1 uses a ln|B| − a ln|A| when A,B same sign
- Quadratic mode covers many Calc I homework problems
- Compare with Riemann-sum approximations
Calculation logic
Uses antiderivatives of the selected polynomial/power form and evaluates F(B)−F(A).
Result is signed area; portions below the axis contribute negatively.
Area Under the Curve Calculator FAQ
Common questions about this calculator and how to use the results.
What if n = −1?
The tool uses logarithms when A and B have the same sign.
Power vs quadratic?
Power is a single monomial; quadratic includes three terms.
Can A > B?
Yes—the integral flips sign.
Are answers exact?
Numeric evaluation is formatted; simple powers use the closed antiderivative.
Is this free?
Yes.