习题解答 28 三重积分的概念与计算(157-158页)ppt课件.ppt

三重积分的概念与计算 2013 4 15 1 2 3 with plots a sqrt 5 1 2 u x y sqrt x 2 y 2 v x y 1 x 2 y 2 qumian1 plot3d u x y x a a y sqrt a 2 x 2 sqrt a 2 x 2 color yellow qumian2 plot3d v x y x a a y sqrt a 2 x 2 sqrt a 2 x 2 color green quxian spacecurve a cos t a sin t u a cos t a sin t t 0 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 orientation 20 60 4 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 s 2 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 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 5 6 7 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 int int f x y z z z1 x y z2 x y y y1 x y2 x x x1 x2 8 9 with 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 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 orientation 55 68 10 11 f x y z x z 1 y 2 x1 0 x2 1 y1 x x 2 y2 x 1 z1 x y 0 z2 x y 1 y 2 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 12 13 with plots qumian1 plot3d 0 y z y 0 1 z 0 1 y 2 color yellow qumian2 plot3d x y 0 x 0 1 y x 2 1 color green qumian3 plot3d x x 2 z x 0 1 z 0 1 x 4 color brown qumian4 plot3d x y 1 y 2 x 0 1 y x 2 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 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 14 15 f x y z exp abs z theta1 0 theta2 2 Pi r1 theta 0 r2 theta sqrt 1 z 2 z1 x y 1 z2 x y 1 Int Int Int f x y z r r r1 theta r2 theta theta theta1 theta2 z z1 z2 int int int f x y z r r r1 theta r2 theta theta theta1 theta2 z z1 z2 16 17 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 y y1 x y2 x x x1 x2 f 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 18 with 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 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 SCUMATH2008 color grey display qumian pingmian1 pingmian2 text xyz scaling constrained 以下曲面所围成的立体 19 20 在D1上 在D2上 21 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 style 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 22 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 0 0 u 1 1 1