calculus
posted by sol .
find the volume of the solid bounded above by the surface z=f(x,y) and below by the plane region R
f(x,y)= 42xy; R{(x,y)0<x<1;0<y<2

this is pretty straightforward. Nice rectangular base.
v = ∫∫R f(x,y) dA
= ∫[0,1]∫[0,2] 42xy dy dx
= ∫[0,1] (4y  2xy  1/2 y^2)[0,2] dx
= ∫[0,1] (64x) dx
= (6x  2x^2)[0,1]
= 4