Skip to main content
Calcimator

Integral Calculator

Calculate definite integrals of polynomial, trigonometric, and exponential functions over any interval.

Inputs

Results

Definite Integral

0.33333

Absolute Area0.33333
How to Use This Calculator
  1. Select the Function Type (polynomial, trig, exponential) and enter the coefficient and exponent parameters.
  2. Enter the lower bound (a) and upper bound (b) for a definite integral; the result is the signed area between f(x) and the x-axis.
  3. Polynomial integrals are computed exactly using the power rule: ∫xⁿ dx = xⁿ⁺¹/(n+1).
  4. Trigonometric and exponential integrals are computed analytically using standard antiderivative formulas.
  5. A positive result means more area is above the x-axis in [a,b]; a negative result means more area is below.
  6. The shaded chart shows the region of integration so you can verify bounds and visualize the area.

How the result changes with Upper Bound (b)

Upper Bound (b)Definite Integral
-80-170,666.66667
-30-9,000
309,000
80170,666.66667

What each input means

Function Type
Type of function to integrate
Coefficient (c)
Leading coefficient
Parameter (n)
Exponent for polynomial, frequency for trig, rate for exponential
Lower Bound (a)
Lower limit of integration
Upper Bound (b)
Upper limit of integration

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Function Type = 1, Coefficient (c) = 1, Parameter (n) = 2, Lower Bound (a) = 0 = 5 input(s) provided
  2. Calculate Definite Integral
    Definite Integral
    0.33333 = 0.33333

Engine last updated . Checked against 6 independently-derived tests — how we verify calculators.

Related Calculators

The questions that sit next to this one — chosen by subject, including calculators filed under a different category.

Calculus Tools

Area Under Curve Calculator

Approximate the area under f(x) = x² using trapezoidal, Simpson's, or midpoint rule. Compare with the exact answer.

Calculus Tools

Derivative Calculator

Calculate the derivative of polynomial, trigonometric, exponential, and logarithmic functions at any point.

Math & Statistics

Advanced Graphing Calculator

Plot functions, compute calculus operations, and explore advanced math with interactive graphs.

Decorative Concrete

Integral Color Calculator

Calculate iron-oxide pigment weight for integrally colored concrete based on volume, mix design, and color intensity.

Calculus Tools

Arc Length Calculator

Calculate the arc length of linear, quadratic, and circular curves between two points using numerical integration.

More in Math & Statistics.