Using Gauss formula, we can find the surface fraction ∮ XY ^ 2dydz + YZ ^ 2dzdx + ZX ^ 2dxdy, where ∑ is the outside of the sphere x ^ 2 + y ^ 2 + Z ^ 2 = R ^ 2 The reference answer is 4 π R ^ 5 / 5. But I'm always 2 π R ^ 5 / 5 My score is settled on the spot. My adoption rate is 100% Let P = XY & # 178;, q = YZ & # 178;, r = ZX & # 178; ∵αP/αx=y²,αQ/αy=z²,αR/αz=x² The original formula = ∫ ∫ (α P / α x + α Q / α y + α R / α z) dxdydz is obtained from Gauss formula =∫∫∫(x²+y²+z²)dxdydz =∫dθ∫sinφdφ∫r^4dr =(2π)[0--(1)](R^5/5-0) =2πR^5/5

Using Gauss formula, we can find the surface fraction ∮ XY ^ 2dydz + YZ ^ 2dzdx + ZX ^ 2dxdy, where ∑ is the outside of the sphere x ^ 2 + y ^ 2 + Z ^ 2 = R ^ 2 The reference answer is 4 π R ^ 5 / 5. But I'm always 2 π R ^ 5 / 5 My score is settled on the spot. My adoption rate is 100% Let P = XY & # 178;, q = YZ & # 178;, r = ZX & # 178; ∵αP/αx=y²,αQ/αy=z²,αR/αz=x² The original formula = ∫ ∫ (α P / α x + α Q / α y + α R / α z) dxdydz is obtained from Gauss formula =∫∫∫(x²+y²+z²)dxdydz =∫dθ∫sinφdφ∫r^4dr =(2π)[0--(1)](R^5/5-0) =2πR^5/5

The original formula = ∫ ∫ (α P / α x + α Q / α y + α R / α z) dxdydz
=∫∫∫(x²+y²+z²)dxdydz
=∫ D θ∫ sin φ D φ∫ R ^ 4DR
=(4π)[0--(1)](R^5/5-0)
=4πR^5/5