习题解答 28 三重积分的概念与计算(157158页)

1、三重积分的概念与计算三重积分的概念与计算2013.4.15with(plots):a:=(sqrt(5)-1)/2: u:=(x,y)-sqrt(x2+y2): v:=(x,y)-1-x2-y2:qumian1:=plot3d(u(x,y),x=-a.a,y=-sqrt(a2-x2).sqrt(a2-x2),color=yellow):qumian2:=plot3d(v(x,y),x=-a.a,y=-sqrt(a2-x2).sqrt(a2-x2),color=green):quxian:=spacecurve(a*cos(t),a*sin(t),u(a*cos(t),a*sin(t),t=0.

2、2*Pi,color=red,thickness=4): x_axis:=plot3d(u,0,0,u=-1/2.1/2,v=0.0.01,thickness=3):y_axis:=plot3d(0,u,0,u=-1/2.1/2,v=0.0.01,thickness=3):z_axis:=plot3d(0,0,u,u=-.2.1.2,v=0.0.01,thickness=3):xyz:=display(x_axis,y_axis,z_axis,thickness=3):display(qumian1,qumian2,quxian,xyz,scaling=constrained,orientat

3、ion=20,60);with(plots):R:=(sqrt(5)-1)/2:qumian1:=plot3d(s*cos(t),s*sin(t),s,t=0.2*Pi,s=0.R,color=yellow):qumian2:=plot3d(s*cos(t),s*sin(t),1-s2,t=0.2*Pi,s=0.R,color=green):x_axis:=plot3d(u,0,0,u=-1/2.1/2,v=0.0.01,thickness=3):y_axis:=plot3d(0,u,0,u=-1/2.1/2,v=0.0.01,thickness=3):z_axis:=plot3d(0,0,u

4、,u=-.2.1.2,v=0.0.01,thickness=3):xyz:=display(x_axis,y_axis,z_axis,thickness=3):display(qumian1,qumian2,xyz,scaling=constrained,orientation=33,68) f:=(x,y,z)-y*cos(x+z):x1:=0:x2:=Pi/2:y1:=x-0:y2:=x-sqrt(x):z1:=(x,y)-0:z2:=(x,y)-Pi/2-x:Int(Int(Int(f(x,y,z),z=z1(z,y).z2(z,y),y=y1(x).y2(x),x=x1.x2)=int

5、(int(int(f(x,y,z),z=z1(x,y).z2(x,y),y=y1(x).y2(x),x=x1.x2);d02d0 xd02zy()cosxzz y x21612with(plots):qumian1:=plot3d(x,0,z,x=0.Pi/2,z=0.Pi/2-x,color=yellow):qumian2:=plot3d(x,y,0,x=0.Pi/2,y=0.sqrt(x),color=green):qumian3:=plot3d(x,sqrt(x),z,x=0.Pi/2,z=0.Pi/2-x,color=brown):qumian4:=plot3d(x,y,Pi/2-x,

6、x=0.Pi/2,y=0.sqrt(x),color=gray):x_axis:=plot3d(u,0,0,u=-1/2.2,v=0.0.01,thickness=3):y_axis:=plot3d(0,u,0,u=-1/2.1,v=0.0.01,thickness=3):z_axis:=plot3d(0,0,u,u=-.2.2,v=0.0.01,thickness=3):xyz:=display(x_axis,y_axis,z_axis,thickness=3):display(qumian1,qumian2,qumian3,qumian4,xyz,scaling=constrained,o

7、rientation=55,68);f:=(x,y,z)-x*z/(1+y)2:x1:=0:x2:=1:y1:=x-x2:y2:=x-1:z1:=(x,y)-0:z2:=(x,y)-1-y2: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);d01dx21d01y2x z()1y2z y x148with(plots):qumian1:=plot3d(0,y,z,y=0.1,z=0.1-y2,col

8、or=yellow):qumian2:=plot3d(x,y,0,x=0.1,y=x2.1,color=green):qumian3:=plot3d(x,x2,z,x=0.1,z=0.1-x4,color=brown):qumian4:=plot3d(x,y,1-y2,x=0.1,y=x2.1,color=gray):x_axis:=plot3d(u,0,0,u=-1/2.1,v=0.0.01,thickness=3):y_axis:=plot3d(0,u,0,u=-1/2.1.5,v=0.0.01,thickness=3):z_axis:=plot3d(0,0,u,u=-.2.1.5,v=0

9、.0.01,thickness=3):xyz:=display(x_axis,y_axis,z_axis,thickness=3):display(qumian1,qumian2,qumian3,qumian4,xyz,scaling=constrained,orientation=55,68);f:=(x,y,z)-exp(abs(z);theta1:=0:theta2:=2*Pi:r1:=theta-0:r2:=theta-sqrt(1-z2):z1:=(x,y)-1:z2:=(x,y)-1:Int(Int(Int(f(x,y,z)*r,r=r1(theta).r2(theta),thet

10、a=theta1.theta2),z=z1.z2)=int(int(int(f(x,y,z)*r,r=r1(theta).r2(theta),theta=theta1.theta2),z=z1.z2);d-11d02 d01z2ezr r z2 f:=(x,y,z)-x:x1:=0:x2:=1:y1:=x-0:y2:=x-(1-x)/(1+x):z1:=(x,y)-0:z2:=(x,y)-x*y: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)

11、,y=y1(x).y2(x),x=x1.x2);d01d01xx1d0y zxz y x2566( )ln 2f:=(x,y,z)-x:x1:=0:x2:=1:y1:=x-(1-x)/(1+x):y2:=x-1-x:z1:=(x,y)-0:z2:=(x,y)-1-x-y: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);d01d1x1x1xd0 1zyxz y x133248( )ln 2with(

12、plots):pingmian1:=implicitplot3d(z=0,x=-.2.1.2,y=-0.2.1.2,z=-1.1,color=grey,style=patchnogrid):pingmian2:=implicitplot3d(z=1-x-y,x=-.2.1.2,y=-0.2.1.2,z=-0.5.1.2,color=green,style=patchnogrid):qumian:=implicitplot3d(z=x*y,x=-.2.1.2,y=-0.2.1.2,z=-1.1.3,color=brown,style=patch):x_axis:=plot3d(u,0,0,u=-

13、1.1.3,v=0.0.01,thickness=3):y_axis:=plot3d(0,u,0,u=-1.1.5,v=0.0.01,thickness=3):z_axis:=plot3d(0,0,u,u=-.3.1.5,v=0.0.01,thickness=3):xyz:=display(x_axis,y_axis,z_axis,thickness=3):text:=textplot3d(0,0,-.8,SCUMATH 2008,color=grey):display(qumian,pingmian1,pingmian2,text,xyz,scaling=constrained);0,1,z

14、zxy zxy 以下曲面所围成的立体：以下曲面所围成的立体：1zxyzxy 1xyxy 11xyx1D2D在在D1上：上：0zxy在在D2上：上：01zxy with(plots):pingmian1:=plot3d(x,y,0,x=0.1,y=0.1-x,color=grey,style=patchnogrid):pingmian2:=plot3d(x,y,1-x-y,x=0.1,y=(1-x)/(1+x).1-x,color=green,style=patchnogrid):qumian:=plot3d(x,y,x*y,x=0.1,y=0.(1-x)/(1+x),color=brown,s

15、tyle=patchnogrid):x_axis:=plot3d(u,0,0,u=-.1.1.1,v=0.0.01,thickness=3):y_axis:=plot3d(0,u,0,u=-.1.1.1,v=0.0.01,thickness=3):z_axis:=plot3d(0,0,u,u=-.1.0.2,v=0.0.01,thickness=3):xyz:=display(x_axis,y_axis,z_axis,thickness=3):display(qumian,pingmian1,pingmian2,xyz,scaling=constrained); with(plots):pingmian:=plot3d(x,y,0,x=0.1,y=0.1-x,color=grey,style=patchnogrid):qumian2:=plot3d(x,(1-x)/(1+x),z,x=0.1,z=0.x*(1-x)/(1+x),color=gold,style=patchnogrid):qumian:=plot3d(x,y,x*y,x=0.1,y=0.(1-x)/(1+x),color=brown,style=patchnogrid):x_axis:=plot3d(u