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Application of Orthogonal Transformation in Integral Calculus of Multivariate Function and Its Mathematical Thinking Method

Integral calculus of multivariate function is formed in the development and application of the ba-sic idea of single variable integral calculus, which is an important teaching module of mathematical analysis. Its calculation often has certain difficulty and skill, which troubles many students. Orthogonal transformation is one of the core contents of advanced algebra and it is also an important method to solve problems. Many scholars have also carried out related research on the application of orthogonal transformation in integral and achieved certain results. Based on this, the paper mainly studies how to skillfully use orthogonal transformation to calculate multiple integral when the integral region is rectangular or cuboid. It also explores the mathematical thinking method of orthogonal transformation in solving these problems, which is very important to the for-mation of students’ thinking concept and methodology.