Definite Integral Calculator (Polynomial)
Exact definite integral of a cubic polynomial.
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ⓘ Live results
Results
- Definite integral
- 2.25
- Antiderivative F(x)
- 0.25x^4 + 0x^3 + -2x^2 + 0x
- F(upper) - F(lower)
- 2.25 - 0
Quick answer
Integrate term by term using x^(n+1)/(n+1), then evaluate at the upper bound minus the lower bound.
∫[a,b] f(x)dx = F(b)-F(a)
How to use the Definite Integral Calculator (Polynomial)
- 1Enter the polynomial coefficients up to cubic (set unused ones to 0).
- 2Enter the lower and upper bounds of integration.
- 3The tool integrates term by term and subtracts F(lower) from F(upper).
Worked example
Using the values the calculator loads with:
Inputs
- Coefficient of x^31
- Coefficient of x^20
- Coefficient of x-4
- Constant0
- Lower bound0
- Upper bound3
Results
- Definite integral2.25
- Antiderivative F(x)0.25x^4 + 0x^3 + -2x^2 + 0x
- F(upper) - F(lower)2.25 - 0
Frequently asked questions
What does a negative integral mean?
The curve lies below the x-axis on average over that interval.
Can I integrate non-polynomial functions?
Use the numerical Simpson's rule tool for functions without a simple closed form here.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.