用向量函数证明积分换元公式

Vector-valued Functions and Substitution Formula for Integrations

运用二元向量函数和三元向量函数证明二重积分和三重积分的换元公式,推导曲面的表面积公式,并计算第二类曲面积分.

This article demonstrates the use of vector-valued functions to derive substitution formulas for double and triple integrals. Similarly, we deduce the formulas for surface area, including formula for the surface integrals of the second type.