I am asked to calculate the mass of the region bounded above by the plane
(2x + 3y - z = 2) and below by the triangle on the xy-plane with vertices
(0,2),(1,0),(4,0). The density is proportional to the distance from the plane to the xy-plane, so the function is
d(x,y,z) = kz.
My limits are:
0 ≤ z ≤ (2x + 3y - 2)
(1 - 0.5y) ≤ x ≤ (4 - 2y)
0 ≤ y ≤ 2.
My code is:
but Mathematica doesn’t return a number (if I’m correct, it should be 19k).
Instead I get:
However if I integrate the function step-by-step:
I do get a numerical value.
Is there a certain syntax that Mathematica requires that I’m not aware of?