習(xí)題解答-28-三重積分的概念與計(jì)算(157-158頁)(參考版)
2025-07-29 13:25本頁面
【正文】 。 0 , 1 ,z z x y z x y? ? ? ? ?以下曲面所圍成的立體： 1z x yz x y???? ? ??1x y x y? ? ? ?11xyx???1D2D在 D1上： 0 z x y??在 D2上： 01z x y? ? ? ?with(plots): pingmian1:=plot3d([x,y,0],x=0..1,y=0..1x,color=grey,style=patchnogrid): pingmian2:=plot3d([x,y,1xy],x=0..1,y=(1x)/(1+x)..1x,color=green,style=patchnogrid): qumian:=plot3d([x,y,x*y],x=0..1,y=0..(1x)/(1+x),color=brown,style=patchnogrid): x_axis:=plot3d([u,0,0],u=..,v=0..,thickness=3): y_axis:=plot3d([0,u,0],u=..,v=0..,thickness=3): z_axis:=plot3d([0,0,u],u=..,v=0..,thickness=3): xyz:=display(x_axis,y_axis,z_axis,thickness=3): display(qumian,pingmian1,pingmian2,xyz,scaling=constrained)。 ?? ?d???01d???0?? ?1 x?? ?x 1d???0y zx z y x ?? ?256 6 ( )ln 2f:=(x,y,z)x: x1:=0:x2:=1: y1:=x(1x)/(1+x):y2:=x1x: z1:=(x,y)0:z2:=(x,y)1xy: Int(Int(Int(f(x,y,z),z=z1(z,y)..z2(z,y)),y=y1(x)..y2(x)),x=x1..x2) =int(int(int(f(x,y,z),z=z1(x,y)..z2(x,y)),y=y1(x)..y2(x)),x=x1..x2)。 theta1:=0:theta2:=2*Pi: r1:=theta0:r2:=thetasqrt(1z^2): z1:=(x,y)1:z2:=(x,y)1: Int(Int(Int(f(x,y,z)*r,r=r1(theta)..r2(theta)),t
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