Definite Integral Calculator (Numerical)
Numerically evaluate a definite integral of f(x) between two limits using Simpson’s rule, with the formula, step size and a trapezoidal cross check.
Runs on your device
Result
Results appear here after you select “Integrate”.
What it does
Type a function of x and the limits. Simpson’s rule fits parabolas through the curve and is exact for polynomials up to degree three. The result is compared with the trapezoidal rule so you can judge accuracy.
How to use it
- Enter f(x), for example x^2 * sin(x).
- Enter the lower and upper limits (pi is allowed).
- Read the value and the working.
Example
∫₀^π sin x dx = 2 exactly. Select Try an example above to see it.
When it helps
- Checking integration homework answers.
- Areas under curves in physics and engineering.
- Signal energy and RMS calculations.
Questions
Does it show the antiderivative?
No. It computes the numeric value. Use it to verify the final answer of your hand working.
What about improper integrals or singularities?
If the function is undefined anywhere in the interval, the tool tells you instead of giving a misleading number.
Are trig functions in radians?
Yes. Calculus uses radians.
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