Approximating computation of integrals: romberg nInt

### 10.3.3 Approximating computation of integrals: romberg nInt

The romberg command finds approximate values of integrals using the Romberg method.
nInt is a synonym for rombert.

- romberg takes three mandatory arguments and one optional argument:
  - expr, an expression involving one variable.
  - Optionally, var, the variable (by default x).
  - a,b, two real numbers.
- romberg(expr ⟨,var⟩ a,b) returns an approximated value of the integral ∫abexprdvar. The integrand must be sufficiently regular for the approximation to be accurate, otherwise, romberg returns a list of real values that come from the application of the Romberg algorithm (the first list element is the trapezoid rule approximation, the next ones come from the application of the Euler-MacLaurin formula to remove successive even powers of the step of the trapezoid rule).

#### Example.

Input:

romberg(exp(x^2),x,0,1)

Output:

1.46265174591