The new schemes of calculation of double integrals and triple integrals are proposed in this paper. The formulas in which the double integral is converted into a line integral with respect to the arc length, and the triple integral is converted into a surface integral with respect to the area or a line integral with respect to the arc length are given separately. The effectiveness of the proposed methods is verified by several examples. Under certain conditions, these methods become the normal iterated integrals in Cartesian coordinate system or polar coordinate system, and the commonly used triple iterated integrals in Cartesian coordinate system, Cylindrical coordinate system or Spherical coordinate system. The transformation calculation method promoted in this paper points out the intrinsic relationship among double integral, triple integral, line integral and surface integral, which further enriches the theories of multivariate integrals.
Citation: Rong-jian Ning, Xiao-yan Liu, Zhi Liu. Conversion calculation method of multivariate integrals[J]. AIMS Mathematics, 2021, 6(3): 3009-3024. doi: 10.3934/math.2021183
The new schemes of calculation of double integrals and triple integrals are proposed in this paper. The formulas in which the double integral is converted into a line integral with respect to the arc length, and the triple integral is converted into a surface integral with respect to the area or a line integral with respect to the arc length are given separately. The effectiveness of the proposed methods is verified by several examples. Under certain conditions, these methods become the normal iterated integrals in Cartesian coordinate system or polar coordinate system, and the commonly used triple iterated integrals in Cartesian coordinate system, Cylindrical coordinate system or Spherical coordinate system. The transformation calculation method promoted in this paper points out the intrinsic relationship among double integral, triple integral, line integral and surface integral, which further enriches the theories of multivariate integrals.
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Rong-jian Ning, Xiao-yan Liu, Zhi Liu. Conversion calculation method of multivariate integrals[J]. AIMS Mathematics, 2021, 6(3): 3009-3024. doi: 10.3934/math.2021183
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