设在上半平面D={(x,y)|y>0}内,函数f(x,y)具有连续偏导数,且对任意的 t>0都有f(tx,ty)=t^(-2) f(x,y).证明:对D内的任意分段光滑的有向简单闭曲线L,都有∮yf(x,y)dx - xf(x,y)dy=0.(积分区域为L)
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![设在上半平面D={(x,y)|y>0}内,函数f(x,y)具有连续偏导数,且对任意的 t>0都有f(tx,ty)=t^(-2) f(x,y).证明:对D内的任意分段光滑的有向简单闭曲线L,都有∮yf(x,y)dx - xf(x,y)dy=0.(积分区域为L)](/uploads/image/z/4048225-25-5.jpg?t=%E8%AE%BE%E5%9C%A8%E4%B8%8A%E5%8D%8A%E5%B9%B3%E9%9D%A2D%3D%7B%EF%BC%88x%2Cy%29%7Cy%EF%BC%9E0%7D%E5%86%85%2C%E5%87%BD%E6%95%B0f%28x%2Cy%29%E5%85%B7%E6%9C%89%E8%BF%9E%E7%BB%AD%E5%81%8F%E5%AF%BC%E6%95%B0%2C%E4%B8%94%E5%AF%B9%E4%BB%BB%E6%84%8F%E7%9A%84+t%EF%BC%9E0%E9%83%BD%E6%9C%89f%28tx%2Cty%29%3Dt%5E%28-2%29+f%28x%2Cy%29.%E8%AF%81%E6%98%8E%EF%BC%9A%E5%AF%B9D%E5%86%85%E7%9A%84%E4%BB%BB%E6%84%8F%E5%88%86%E6%AE%B5%E5%85%89%E6%BB%91%E7%9A%84%E6%9C%89%E5%90%91%E7%AE%80%E5%8D%95%E9%97%AD%E6%9B%B2%E7%BA%BFL%2C%E9%83%BD%E6%9C%89%E2%88%AEyf%28x%2Cy%29dx+-+xf%28x%2Cy%29dy%3D0.%28%E7%A7%AF%E5%88%86%E5%8C%BA%E5%9F%9F%E4%B8%BAL%29)
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