∫∫xdxdy,其中D为x^2+y^2>=2,x^2+y^2<=2x.计算二重积分

2025-01-21 11:27:48
推荐回答(1个)
回答1:

做个提示吧:
x^2+y^2=2,x^2+y^2=2x的交点(1,1)用极坐标并考虑对称性:
∫∫xdxdy
=2∫(0,π/4)cosθdθ∫(√2,2cosθ)r^2dr
=(2/3)∫(0,π/4)(8(cosθ)^4-2√2cosθ)dθ