帮看个曲面积分,求教育……∫∫(xy+yz+xz)dS被积曲面是圆锥面z=根号（x^2+y^2）被曲面x^2+y^2=2ax所割下的部分,

Question

帮看个曲面积分,求教育……
∫∫(xy+yz+xz)dS 被积曲面是圆锥面z=根号（x^2+y^2）被曲面x^2+y^2=2ax所割下的部分,

Answer 1

dS=√2dxdy
∫∫(xy+yz+xz)dS
=∫∫(x √(x²+y²))√2dxdy :D x^2+y^2≤2ax
=2∫[0,π/2]dθ∫ [0,2acosθ] √2ρ³cosθdρ
=8√2a^5 ∫[0,π/2]cos^(5)θdθ
=8√2(a^5)* 4*2/(5*3)
=64√2(a^5)/3