### 8.3.3 Approximate computation of integrals : romberg nInt

romberg or nInt takes as arguments : an expression
ex, the variable name of this expression (by default x), and
two real values a,b.

romberg(ex,x,a,b) or nInt(ex,x,a,b) computes an approximated
value of the integral ∫_{a}^{b} ex dx using the Romberg method. The
integrand must be sufficiently regular for the approximation to
be accurate. Otherwise, romberg returns a list of real values,
that comes 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).

Input :

romberg(exp(x`^`

2),x,0,1)

Output :

1.46265174591