数学分析中重积分的解法探讨

On the Calculation Methods of Multiple Integrals in Mathematical Analysis

摘要: 重积分的解法是数学分析课程中的重要内容，本文利用极坐标变换衍生出一种解法，将重积分转化成为关于定积分和曲面(线)积分的累次积分，即：先固定半径在球面(圆)上积分，再对半径积分。通过该解法，能加深学生对重积分的几何直观理解。

Abstract: The calculation methods for multiple integrals constitute an important part of Mathematical Analysis. This paper proposes a new approach derived from polar coordinate transformation, which converts multiple integrals into iterated integrals involving definite integrals and surface/line integrals. Specifically, integration is first performed over a sphere (circle) with a fixed radius, followed by integration with respect to the radius. This method helps students develop clearer geometric intuition for multiple integrals.