Integral Calculator
Compute the definite integral of any function between two limits.
All calculations happen locally in your browser — nothing is uploaded, stored or tracked.
Type your function
e.g. x^2, sin(x), or e^(-x^2).
Set the limits
The lower and upper bounds of integration.
Calculate
Get the integral and the average value over the interval.
What Is an Integral Calculator?
A definite integral measures the area between a function's curve and the x-axis over an interval — and, more deeply, it accumulates the function's values. It is the inverse operation of differentiation, used throughout physics, engineering and economics.
This calculator evaluates definite integrals numerically using Simpson's rule with a large number of subintervals, which is exact for polynomials up to cubic degree and extremely accurate for smooth functions.
How It Works
The interval [a, b] is split into 2,000 equal subintervals and the function is sampled at each point. Because Simpson's rule weights alternating samples by 4 and 2, it captures curvature far better than simple rectangles. The calculator also reports the average value of the function over the interval.
Your data never leaves your device.
Every calculation on this site runs in your browser using vanilla JavaScript. Nothing is uploaded, stored or tracked.
- 100% local, client-side calculations
- No data stored on any server
- No tracking, no analytics, no ads scripts
- Works offline once loaded
Frequently Asked Questions
What is a definite integral?
It is the signed area under a curve between two limits — positive where the function is above the axis, negative where it is below.
Is the result exact?
It is numerical, using Simpson's rule with 2,000 subintervals — accurate to many decimal places for smooth functions and exact for polynomials up to degree 3.
Can I integrate trigonometric functions?
Yes — sin, cos, tan and their inverses are all supported in the function syntax.
What does the average value mean?
It is the integral divided by the interval width: the constant height that would give the same area over the same interval.
How do I type an exponential function?
Use e^(x) or exp(x). For example e^(-x^2) works as written.