Integration

ALIAS provides various procedures for the certified calculation of definite integrals. These procedures will return a range that is guaranteed to include the real value of the integral. The width of the range will be lower than the global variable `ALIAS/fepsilon`. In the current implementation only finite bounds may be used.

Some of the following procedures involve the use of the derivatives and you should be careful when the interval evaluation of these derivative cannot be performed. For example when considering $e^x+2\sqrt{x}+1$ you should not 0 in the integration domain. In that case you should integrate around 0 by using the Integrate problem while using another procedure for the remaining part of the domain.