阐述了矢量场沿一阶无穷小线段的线积分虽然也是一阶无穷小量，但特殊情况下要求计算精度必须达到二阶无穷小量，为此目的需要把一阶无穷小线段分成无穷多个二阶无穷小线元来计算线积分，并且给出如此计算所得结果遵循的规律，即二阶无穷小精度下矢量场沿一阶无穷小线段的线积分定理.最后介绍了这个定理在旋度理论和电磁场切向边值关系理论中的应用.

This paper expounds though the line integral that the vector field along the first-order infinitesimal line is also the first-order dimensionless，but in particular cases demand the computational accuracy must achieve the second-order dimensionless. For this purpose，we need to divide the first-order infinitesimal line segment into infinitely many second-order infinitesimal line element to calculate the line integral，and give the law that followed by the result that obtained through such calculation: the theorem of vector field along first-order infinitesimal line segment’s line integral under second-order infinitesimal accuracy. We introduce application of this theorem in curl theory and in the theory of electromagnetic field tangential boundary value relations.