正确使用高斯公式计算曲面积分

Correctly Using the Gauss formula to Calculate Surface Integral

指出了同济大学第五版《高等数学》教材的配套参考书上([1]、[2]、[3]、[4]、[5]),关于计算曲面积分一题的解法错误所在,分析了错误的原因,给出了正确解法。告诫学生使用高斯公式计算曲面积分时一定不能忽视条件,否则可能导致错误。

This article indicates one wrong way to solve the problem of calculating surface integral ,which appears in the reference of Higher Mahematics （the fifth edition）,teaching material compiled by Tongji University ,analyses the cause and gives the right way. It reminds the learners to notice the formula premise when using Gauss Formula,to avoid obtain a wrong result.