(872, #5) Evaluate the iterated integral

Solution:

lprint(int( z*sin(y), x));
lprint(int( z*sin(y), x= 0..sqrt(4-z^2)));
z*sin(y)*x
(4-z^2)^(1/2)*z*sin(y)

lprint( int(int( z*sin(y), x= 0..sqrt(4-z^2)), z ));
lprint( int(int( z*sin(y), x= 0..sqrt(4-z^2)), z = 0..2 ));
-1/3*(4-z^2)^(3/2)*sin(y)
8/3*sin(y)

lprint( int(int(int( z*sin(y),x = 0..sqrt(4-z^2)), z = 0..2 ), y));
lprint( int(int(int( z*sin(y),x = 0..sqrt(4-z^2)), z = 0..2 ), y = 0..Pi));
-8/3*cos(y)
16/3

by: gm