Softonic

Integral Calculator

Step 1 / 4 Integral estimate

Choose one of the built-in functions, set the lower and upper limits, and get a numerical estimate of the definite integral. The calculator uses composite Simpson’s rule, so it is best for smooth functions on a finite interval where the function is defined throughout.

How to estimate a definite integral

  1. 1

    Choose the function

    Pick `e^x`, `sin(x)`, `cos(x)`, `x²`, `x³`, `√x`, `1/x` or `ln(x)` from the function buttons.

  2. 2

    Set the interval

    Enter the lower limit `a` and upper limit `b`. For `√x` and `ln(x)`, keep the interval positive; for `1/x`, do not cross zero.

  3. 3

    Choose precision

    Set an even number of subintervals. The tool automatically rounds an odd value up to the next even value because Simpson's rule works in pairs.

  4. 4

    Read the estimate

    The result is the signed area from `a` to `b`, with a summary you can copy for homework, checking or quick analysis.

What this calculator does

This is a numerical definite-integral calculator. It estimates

∫_a^b f(x) dx

for a selected function over a finite interval. It does not solve indefinite integrals, produce symbolic antiderivatives or prove convergence for improper integrals.

Supported functions

Function Domain to use Useful test interval
e^x any real x [0, 1]
sin(x) any real x [0, π]
cos(x) any real x [0, π/2]
x² any real x [0, 3]
x³ any real x [-1, 1]
√x x >= 0 [0, 4]
1/x interval must not include 0 [1, 2]
ln(x) x > 0 [1, e]

Simpson’s rule in this tool

Composite Simpson’s rule splits [a, b] into an even number n of equal subintervals. With h = (b-a)/n and x_i = a + i h, the estimate is:

∫_a^b f(x) dx ≈ h/3 [f(x_0) + 4f(x_1) + 2f(x_2) + ... + 4f(x_{n-1}) + f(x_n)]

The calculator lets you choose between 2 and 100000 subintervals. If you enter an odd number, it uses the next even number so the Simpson weights line up correctly.

How to read the result

  • Signed area matters. Area below the x-axis subtracts from area above it.
  • Reversed limits change the sign. Switching a and b multiplies the estimate by -1.
  • More subintervals usually help on smooth curves. They do not fix a discontinuity, a vertical asymptote or a domain error.
  • Domain limits still apply. √x needs non-negative inputs, ln(x) needs positive inputs, and 1/x cannot be evaluated at zero.

When this is not enough

Use a symbolic algebra system or a full calculus workflow when you need an exact antiderivative, an indefinite integral, a proof for an improper integral or rigorous error bounds. Use this calculator when you need a fast numerical estimate for the functions it supports.

Frequently Asked Questions

No. It is a numerical estimate from composite Simpson’s rule. For smooth functions, increasing the subinterval count usually improves the estimate.

This version uses the function buttons shown in the tool: e^x, sin(x), cos(x), x², x³, √x, 1/x and ln(x).

Simpson’s rule fits parabolic arcs over pairs of subintervals. If you enter an odd count, the calculator rounds it up to the next even number.

The interval may leave the function’s domain, for example √x below zero, ln(x) at zero or below, or 1/x across zero. Adjust the bounds and try again.

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