## Section: New Results

### Formally Certified Computation of Improper Definite Integrals

Assia Mahboubi and Thomas Sibut-Pinote, in collaboration with Guillaume Melquiond (Toccata), have pursued their work on the certified computation of intervals approximating the values of definite integrals involving elementary mathematical functions. This library provides an automated tool that builds a formal proof of the correctness of the output, that is, a formal proof that the interval contains the mathematical values and a formal proof of the integrability of the input function on the input interval. This tool has been extended this year, and it can now deal with improper integrals, that is, integrals whose bounds are infinite or singularities of the integrand. The methodology, the implementation and benchmarks have been described in [13].