# find the mass of the solid

• Jan 1st 2011, 09:46 AM
darkbaser
find the mass of the solid
(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
• Jan 1st 2011, 10:41 AM
FernandoRevilla
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
• Jan 1st 2011, 11:17 AM
darkbaser
in some detail would be so much nice iam thankful for you
• Jan 1st 2011, 11:30 AM
Jameson
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?
• Jan 1st 2011, 11:35 AM
darkbaser
no i dont our doctor just gaved it to us and he didnt solve them :S all i get from the last post is the equation but the limits of intgration i dont know them and {k} is something constant or what ???
• Jan 1st 2011, 12:00 PM
mr fantastic
Quote:

Originally Posted by darkbaser
no i dont our doctor just gaved it to us and he didnt solve them :S all i get from the last post is the equation but the limits of intgration i dont know them and {k} is something constant or what ???

k is obviously a proportionality constant:

Quote:

Originally Posted by darkbaser
(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

Quote:

Originally Posted by darkbaser
no i dont our doctor just gaved it to us and he didnt solve them :S all i get from the last post is the equation but the limits of intgration i dont know them [snip]

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.
• Jan 1st 2011, 12:14 PM
Jameson
Quote:

Originally Posted by darkbaser
no i dont our doctor just gaved it to us and he didnt solve them :S all i get from the last post is the equation but the limits of intgration i dont know them and {k} is something constant or what ???

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?