坐标系转换:
u=x-1
v=y
D->u^2+v^2=1
x²+y²-3 = (u+1)^2+v^2+3=u^2+2u+v^2-2
∫∫(x²+y²-3)dxdy=∫∫u^2+2u+v^2-2dudv
其中:
∫∫-2dudv=-2*面积=-2π
∫∫2ududv=0 由奇偶性可得
∫∫u^2+v^2dudv=2∫∫u^2dudv 由字母的伦焕性可得
令u=rcosQ
v=rsinQ
2∫∫u^2dudv=2∫∫u^2dudv
=2 积分[0,2π]dQ 积分[0,1] r^3cos^2(Q)dr=π/2
于是院士=π/2-2π=3π/2