极坐标变换 x=rc0s,y=rsin6,0≤6≤2π,0≤r<+∞ 是我们十分熟悉的。除原点与正实轴外,它是一一对应的,这时 a(x, y)cos -rsin e a(r, 0) sin e rcos e 例1333计算』smxx2+yddy,其中D=(xy)x2+y2sl D 解引入极坐标变换x=rcosθ,y= rsin e,那么D对应于区域 D={(,0)0≤r≤1,0≤O≤2π}。因此 s sin(a x'+y)drdy=(sin t)a(x, ))(sin tr)rdrde 2兀 = de l sin(r)rdr=2