%0 Journal Article
%T 高维视角下的积分问题&#65306;升维方法与技巧的统一分析<br>Integral Problems from a High-Dimensional Perspective: A Unified Analysis of Dimensional Elevation Methods and Techniques
%A 贾瑞玲
%A 滕吉红
%A 孙铭娟
%J Advances in Applied Mathematics
%P 371-376
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.145266
%X 经典的一维积分问题常因复杂性或隐蔽性难以揭示本质特征&#65292;本文通过将低维问题嵌入高维空间进行重构&#65292;借助多维积分理论(如积分换序、参数化技巧、积分号下求导等)进行求解&#65292;充分展现了高维理论对低维问题的统一化解题能力。这不仅为经典积分难题提供了全新的解决路径&#65292;还为跨学科问题的高维建模提供了重要的理论启示&#65292;拓展了高维方法在不同领域的应用前景。<br>Classical one-dimensional integral problems often struggle to reveal their essential characteristics due to inherent complexity or hidden structures. This study reconstructs these low-dimensional challenges by embedding them into higher-dimensional spaces, employing multidimensional integral theories (such as integration order interchange, parameterization techniques, and differentiation under the integral sign). This approach fully demonstrates the unified problem-solving capabilities of high-dimensional frameworks for low-dimensional issues. The methodology not only provides innovative solutions to classical integration conundrums, but also offers critical theoretical insights for high-dimensional modeling of interdisciplinary problems, significantly expanding the application potential of high-dimensional methods across diverse fields.
%K 定积分&#65292
%K 含参变量的反常积分&#65292
%K 重积分&#65292
%K 升维思想<br>Definite Integral
%K Improper Integral with Parameter
%K Multiple Integral
%K Dimensional Elevation Concept
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=115575