Integral Calculator
Compute definite and indefinite integrals of polynomial, trig, exponential and log terms.
About Integral Calculator
Computes the definite integral ∫[a,b] f(x)dx numerically using composite Simpson's 1/3 rule. This provides O(h⁴) accuracy for smooth functions. Supports any expression the parser can evaluate. For indefinite integrals, the numerical value represents the net signed area from a to b.
Formula
Simpson's rule
∫[a,b] f(x)dx ≈ (h/3)[f(a) + 4f(a+h) + 2f(a+2h) + ... + f(b)]
- a
- Lower bound
- b
- Upper bound
- h
- (b-a)/n
- n
- Number of subintervals (even)
Worked example
With the default values below, Integral Calculator returns ∫f(x)dx of 12.33539937. Change any input above and every figure here is recalculated in your browser.
Inputs used
- f(x)
- x^2 + sin(x)
- Lower bound (a)
- 0
- Upper bound (b)
- 3.14159
- Subintervalsaccepts 2–100,000
- 1,000
Results
- ∫f(x)dx
- 12.33539937
- Method
- Composite Simpson's rule with 1000 subintervals
Step by step
- 1Values used
- 2Simpson's rule
- 3∫f(x)dx= 12.33539937
- 4Method= Composite Simpson's rule with 1000 subintervals
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How many subintervals should I use?
For most smooth functions, 100-1000 subintervals give excellent accuracy. Increase for highly oscillatory functions.
Can I compute improper integrals?
Not directly — use the Improper Integral Calculator which handles infinite limits via adaptive truncation.