Sollya User's Manual

Name:

integral computes an interval bounding the integral of a function on an interval.

Usage:

integral(f,I) : (function, range) -> range

Parameters:

f is a function.
I is an interval.

Description:

integral(f,I) returns an interval J such that the exact value of the integral of f on I lies in J.
This command is safe but very inefficient. Use dirtyintegral if you just want an approximate value.
The result of this command depends on the global variable diam. The method used is the following: I is cut into intervals of length not greater then d*|I| where d is the value of global variable diam. On each small interval J, an evaluation of f by interval is performed. The result is multiplied by the length of J. Finally all values are summed.

Example 1:

   > sin(10);
   -0.54402111088936981340474766185137728168364301291621
   > integral(cos(x),[0;10]);
   [-0.54710197983579690224097637163525943075698599257332;-0.54094015130013183848150540881373370744053741191728]
   > diam=1e-5!;
   > integral(cos(x),[0;10]);
   [-0.54432915685955427101857780295936956775293876382777;-0.54371306401249969508039644221927489010425803173555]