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Calculation Machine

Definite Integral Calculator (Polynomial)

Exact definite integral of a cubic polynomial.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ 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.

The formula

∫[a,b] f(x)dx = F(b)-F(a)

Worked example

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

Result

  • Definite integral2.25
  • Antiderivative F(x)0.25x^4 + 0x^3 + -2x^2 + 0x
  • F(upper) - F(lower)2.25 - 0

How to use the Definite Integral Calculator (Polynomial)

  1. 1Enter the polynomial coefficients up to cubic (set unused ones to 0).
  2. 2Enter the lower and upper bounds of integration.
  3. 3The tool integrates term by term and subtracts F(lower) from F(upper).

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