(872, #1) Evaluate the integral

where B = {(x,y,z) : 0 <= x <= 1, -1 <= y <= 2, 0 <= z <= 3}..

Solution: We have

The step-by-step evaluation of the integral is given below. The first line in each group is the indefinite integral at that step; the second is the definite integral.

lprint(int( x*y*z^2, z));
lprint(int( x*y*z^2,z = 0..3));
1/3*x*y*z^3
9*x*y

lprint( int( int( x*y*z^2, z = 0..3), y));
lprint( int( int( x*y*z^2, z = 0..3), y= -1..2));
9/2*x*y^2
27/2*x

lprint( int(int( int( x*y*z^2,z = 0..3), y = -1..2), x ));
lprint( int(int( int( x*y*z^2,z = 0..3), y= -1..2), x = 0..1));
27/4*x^2
27/4

by: gm