(1) set up a triple integral for the mass of solid that lies under the plane x+2y+z=4 in the first octant if the denisty is proportional to the to the square of distance from the orgin
(1) set up a triple integral for the mass of solid that lies under the plane x+2y+z=4 in the first octant if the denisty is proportional to the to the square of distance from the orgin
The mass is:
$\displaystyle M=\displaystyle\iiint_{T}k({x^2+y^2+z^2)\;dxdydz$
where:
$\displaystyle T \equiv\begin{Bmatrix}0\leq x \leq 4\\\ldots\\\ldots\end{matrix} $
Fernando Revilla
You have been given a big hint. For these problems you need to find an expression for the mass and find the region over which the integral is taken. You've been given the first part and 1/3 of the second. What is the region? Have you seen this kind of problem before?
k is obviously a proportionality constant:
Draw a rough sketch of the surface to see why the integral limits are what they are.
I suggest you go to your textbook (if you don't have a textbook, go to your library and borrow one that covers multi-variable calculus) and review examples of this type of question.
You said this was for a test review. You should know the basic idea of this kind of problem for us to help you. Like mr fantastic said, go re-read your textbook and get familiar with the topic then come back and post your attempt. Someone solving the problem for you won't do you any good if you won't understand it.
Have you done triple integrals before?