Direct Calculating Method for Integral of Multivariate Functions Based on Mathematica

Mathematica is a comprehensive and efficient general mathematical software that integrates numerical and symbolic calculation, graphics and animation, programming and interactive demonstrations. This paper presents the methodology and operational procedures for the direct computation of multiple integrals, curve integrals and surface integrals utilizing Mathematica software. Through the application examples, it can be intuitively seen that this way of calculating multiple integrals with Mathematical software provides a very convenient, fast and effective way to verify the correctness of the integral calculation methods and results.