ｚ→ y → x の順に積分 ∭[D]yzdxdydz =∫[0,a]dx∫[0,√(a²-x²)]ydy∫[0,√(a²-x²-y²)]zdz =1/2∫[0,a]dx∫[0,√(a²-x²)]y(a²-x²-y²)dy =(1/4)∫[0,a](a²－x²)²dx =(2/15)a⁵ 【別解】x=rsinθcosφ y=rsinθsinφ z=rcosθ で変数変換 ヤコビアン：J＝r²sinθ ∭[D]yzdxdydz =∭[D*]rsinθsinφ*rcosθ*r²sinθdrdθdφ =∫[0,a]r⁴dr∫[0,π]sinφdφ∫[0,π/2]sin²θcosθdθ =(2/15)a⁵