Math Help - Area Integrals

1. Area Integrals

Hi

I am really stuck with part of this question.

Part a)i) I have determined the points of intersection, namely 0 and 4.

For part a)ii) I have calculated the boundary area which is 32/3 however I am confused by the wording for the rest of the question. How do I relate it to the density?

Thanks

2. Originally Posted by Ian1779
Hi

I am really stuck with part of this question.

Part a)i) I have determined the points of intersection, namely 0 and 4.

For part a)ii) I have calculated the boundary area which is 32/3 however I am confused by the wording for the rest of the question. How do I relate it to the density?

Thanks
this is just an application of double integrals. the info you need is found in your text in the section on moments, center of mass, or something to that effect.

Let $D$ be a region whose density is given by the function $\rho (x,y)$, then the mass is given by

$m = \iint_D \rho (x,y)~dA$

3. So am I integrating the formula I used to calculate the area twice?

4. Originally Posted by Ian1779
So am I integrating the formula I used to calculate the area twice?
what do you mean find the area twice. you are not required to find the area at all in this problem, you are finding the mass. this is just the integral of the density function, which you were given.

5. Oh I see what you mean now.

Thanks very much.. No wonder I was getting confused!!

6. Originally Posted by Ian1779
Oh I see what you mean now.

Thanks very much.. No wonder I was getting confused!!
yes, make sure you integrate over the given region. it's a double integral