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Publishing Language: Chinese | Open Access

Calculating the double integrals by using parametric equations of boundary curves

Xingtian GONG1( ), Shuwei YANG2
Teaching Department of Mathematics, Lanzhou Technology and Business College, Lanzhou Gansu 730101
School of Science, Lanzhou University of Technology, Lanzhou Gansu 730050
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Abstract

To calculate the double integral, a mapping is proposed with the rectangular region to the integral region D using the parametric equation of the boundary curve of the integral region. Then a formula is proposed and proved for converting the double integral in the cartesian coordinate system into the double integral in parametric coordinates. Finally, the generality and validity of the application of the theory are demonstrated by some examples.

Keywords

double integralboundary curvesparametric equationcoordinate transformation

References

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Journal of Capital Normal University (Natural Science Edition)
Volume 46 Issue 2,
April 2025
Pages 38-42
DOI: 10.19789/j.1004-9398.2025.02.006

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GONG X, YANG S. Calculating the double integrals by using parametric equations of boundary curves. Journal of Capital Normal University (Natural Science Edition), 2025, 46(2): 38-42. https://doi.org/10.19789/j.1004-9398.2025.02.006

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Received: 29 May 2023
Published: 01 April 2025
© The editorial department of Journal of Capital Normal University (Natural Science Edition) 2025.

This is an open access article under the CC BY-NC-ND 4.0 license (https://creativecommons.org/licenses/by-nc-nd/4.0/).