积分区域为半径=1的扇形,角度从-α到α。tanα=1/√2
(x+y)³=x^3+3x^2y+3xy^2+y^3
由对称性:∫∫(3x^2y+y^3)dxdy=0, ∫∫(X+Y)³dxdy=∫∫(x^3+3xy^2)dxdy,用极坐标:
=∫(-α,α)dθ∫(0,1)(r^3(cosθ)^3+3r^3cosθ(sinθ)^2)rdr
=∫...
积分区域为半径=1的扇形,角度从-α到α。tanα=1/√2
(x+y)³=x^3+3x^2y+3xy^2+y^3
由对称性:∫∫(3x^2y+y^3)dxdy=0, ∫∫(X+Y)³dxdy=∫∫(x^3+3xy^2)dxdy,用极坐标:
=∫(-α,α)dθ∫(0,1)(r^3(cosθ)^3+3r^3cosθ(sinθ)^2)rdr
=∫...