数学试题讲解

设正向封闭曲线

C : x^{2} + y^{2} = π

与正向封闭路线

L : | x | + | y | = \frac{π}{4}

, 已知

\oint_{C} \frac{x^{2} y d y - x y^{2} d x}{x^{4} + y^{4}}

= 0

, 则

\oint_{L} \frac{x^{2} y d y - x y^{2} d x}{x^{4} + y^{4}} =