D 为圆 (x-1)^2+(y-1)^2=1 的内部,这个圆与x轴相切于点(1,0),与y轴相切于点(0,1),圆内所有点均在第一象限内.
两个切点(1,0)与(0,1)是边界点,幅角a的范围是0到π/2,而极半径r应该被限制在圆内,即介于圆的左下1/4圆弧和右上3/4圆弧之间.具体方程解不等式：(x-1)^2+(y-1)^2≤1.
有x^2+y^2-2x-2y+1<=0==> r^2 - 2(sin a + cos a)r+1<=0
所以 sin a + cos a - sqrt( sin(2a) ) <=r<=sin a + cos a + sqrt( sin(2a) )(sqrt--根号)
最后,积分化为
∫∫D f(x,y)dxdy = ∫∫D f(x,y)da rdr
= ∫_(0<=a<=π/2) da∫_(sin a + cos a - sqrt(sin(2a))<=r<=sin a + cos a + sqrt(sin(2a))) f(r, a)rdr