Integral Calculator
Compute definite and indefinite integrals of polynomial, trig, exponential and log terms.
Inputs
Enter integrand using x as variable.
∫f(x)dx
12.33539937
Method
Composite Simpson's rule with 1000 subintervals
Step by step
Values used
f(x) = x^2 + sin(x); Lower bound (a) = 0; Upper bound (b) = 3.14; Subintervals = 1,000
Simpson's rule
∫[a,b] f(x)dx ≈ (h/3)[f(a) + 4f(a+h) + 2f(a+2h) + ... + f(b)]
∫f(x)dx
= 12.33539937
Method
= Composite Simpson's rule with 1000 subintervals
How it works
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)
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.