Calculadora de Integrais (polinômio simples)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
∫a·xⁿdx = a·x^(n+1)/(n+1)
About this calculator
This calculator computes the definite integral of a simple polynomial of the form f(x) = a·xⁿ, where 'a' is the coefficient and 'n' the exponent. You provide the lower (x1) and upper (x2) limits and get the area under the curve between these points. The calculation uses the antiderivative: ∫a·xⁿ dx = a·x^(n+1)/(n+1), evaluated at the limits and subtracted. It is ideal for calculus students needing quick results for basic polynomial functions.
How to use: enter the coefficient 'a', exponent 'n', and integration limits x1 and x2. The calculator checks that n ≠ -1 (otherwise the integral would be logarithmic). The result is displayed with up to 4 decimal places. Example: for f(x)=3x² from 1 to 2, the answer is 7.0000. Note that the formula works for real n, and the calculator treats n as a real number.
When to use: in physics problems (work, displacement), engineering (moments of inertia), and mathematics (area under polynomial curves). Caution: this tool does not handle trigonometric, exponential, or logarithmic functions. For more complex integrals, use other calculators. Ensure the exponent is not -1 and that the limits are in correct order (x1 ≤ x2).
Frequently asked questions
What happens if the exponent n equals -1?
The calculator displays an error, because the integral of a/x is a·ln|x|, not covered here. Use a logarithmic integral calculator.
Can I use fractional exponents, like n=0.5?
Yes, the calculator accepts real exponents as long as n ≠ -1. For example, ∫√x dx = (2/3)x^(3/2).
Is the result always the exact area under the curve?
Yes, for simple polynomials, the result is exact (within 4 decimal places). Area below the x-axis is counted as negative.
What if the lower limit is greater than the upper limit?
The calculator does not swap limits. Enter x1 as lower and x2 as upper. If swapped, the result will be the negative of the area.
Does this calculator handle indefinite integrals?
No, it only computes definite integrals (with limits). For indefinite integrals, use another tool that provides the antiderivative.