Section 15.1: Example 4: Iterated integral for f(x,y) = (x^2)(y)

integrate(integrate(x^2*y,y,1,2),x,0,3);

integrate(integrate(x^2*y,x,0,3),y,1,2);

integrate(x^2,x,0,3)*integrate(y,y,1,2);

Example 5: f(x,y) = x - (3)y^2

draw3d(color=green, explicit(0,x,0,2,y,1,2),
       enhanced3d=true, view=[70,20],
       explicit(x-3*y^2,x,0,2,y,1,2),
       xlabel="x", ylabel="y");

integrate(integrate(x-3*y^2,y,1,2),x,0,2);

integrate(integrate(x-3*y^2,x,0,2),y,1,2);

Example 6: f(x,y) = y sin(xy)

draw3d(color=green, explicit(0,x,1,2,y,0,%pi),
       enhanced3d=true, view=[70,20],
       explicit(y*sin(x*y),x,1,2,y,0,%pi),
       xlabel="x", ylabel="y");

integrate(integrate(y*sin(x*y),x,1,2),y,0,%pi);

integrate(integrate(y*sin(x*y),y,0,%pi),x,1,2);