展开全部
z=x代入z=1-x^2-y^2中得
x=1-x^2-y^2,即(x+1/2)^2+y^2=5/4(此区域设为知芦D)
围成的体积
V=∫∫D(1-x^2-y^2-x)dxdy
=∫[0,2π]∫[0,√5/源含2]{1-(rcost-1/2)^2-(rsint)^2-(rcost-1/2)}drdt
(设x=rcost-1/2,y=rsint)
=∫[0,2π]dt∫[0,√5/2](5/搭裂带4-r^2)dr
=2π*(5/4*r-1/3*r^3)|[0,√5/2]
=5π√5/6
x=1-x^2-y^2,即(x+1/2)^2+y^2=5/4(此区域设为知芦D)
围成的体积
V=∫∫D(1-x^2-y^2-x)dxdy
=∫[0,2π]∫[0,√5/源含2]{1-(rcost-1/2)^2-(rsint)^2-(rcost-1/2)}drdt
(设x=rcost-1/2,y=rsint)
=∫[0,2π]dt∫[0,√5/2](5/搭裂带4-r^2)dr
=2π*(5/4*r-1/3*r^3)|[0,√5/2]
=5π√5/6
推荐律师服务:
若未解决您的问题,请您详细描述您的问题,通过百度律临进行免费专业咨询