> BUMPY d 1 C
1
$sin m$ theta $sin n$ phi
5
1
BUMPY := 1 C
sin m q sin n f
5
> RR d subs m = 6, n = 5, BUMPY
RR := 1 C
1
sin 6 q sin 5 f
5
> plot3d RR, theta = 0 ..2 p, phi = 0 ..p, coords = spherical
(1)
(2)
Volume:
2
> r $sin phi
2
r sin f
> int %, rho = 0 ..RR
1
sin f
3
> int %, phi = 0 ..Pi
1
1C
sin 6 q sin 5 f
5
> evalf %
>
3
(4)
2
68
cos 12 q C
99
99
(5)
136
p
99
(6)
4.315723243
(7)
K
> int %, theta = 0 ..2$Pi
(3)
> RR d subs m = 8, n = 7, BUMPY
RR := 1 C
1
sin 8 q sin 7 f
5
> plot3d RR, theta = 0 ..2 p, phi = 0 ..p, coords = spherical
>
>
>
(8)