Romberg Integration Table Calculator

Enter f(x), the interval a to b, and a level count to build the Romberg table R(i,j) and show the best estimate R(n,n).

Input

Enter the integrand f(x), the integration interval, and a level count to build the Romberg table R(i,j). The trapezoidal rule with Richardson extrapolation gives a high-accuracy estimate of the definite integral.

Integrand f(x)

Examples: sin(x), exp(-x^2), 1/(1+x^2). Use x as the variable; pi and e are available.

Lower limit a

Upper limit b

Levels

Number of table rows (1 to 16). More rows give higher accuracy.

Result

The integration interval is invalid. Enter different numbers for a and b.

How it works

The first column R(i,0) is the composite trapezoidal rule with 2 to the power i subintervals.
Later columns use Richardson extrapolation R(i,j) equals R(i,j-1) plus (R(i,j-1) minus R(i-1,j-1)) divided by (4 to the power j minus 1).
The table is lower-triangular (values only where j is at most i); the bottom-right entry R(n,n) is the best estimate.
f(x) supports functions such as sin, cos, exp, log, sqrt and the constants pi and e.
Functions that become non-finite at the endpoints or sample points (those with singularities) cannot be evaluated.

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