企源知识库

求由平面x=0，y=0，x+y=1所围成的柱体被平面z=0及抛物面x²+y²=6-z截得的立体的体积．
【正确答案】：由题意知：V=∫∫_D(6-x²-y²)dxdy =∫₀¹dx∫₀^1-x(6-x²-y²)dy =∫₀¹[6y-x²y-y³/3∣₀^1-x]dx =∫₀¹[6(1-x)-x²(1-x)-(1-x)³/3]dx =∫₀¹(1-x)[-(4/3)x²+(2/3)x+17/3]dx=17/6．