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# Urgent Q watch

1. Find the area of the part of the plane x+y+z=1 which lies in the first octant.

This I managed to do correctly - root 3/2 - which I found by projecting the area onto the x-y plane.. (though I'm getting a minus sign which im not sure about...when i project it onto x-y i see that it is the double integral of root 3 where the line is basically y= -x +1 -- any ideas why?)

It then asks to find its centre of mass using integration..

How would I do this?
THanks
2. anyone?
3. On the face of it, King, this is an odd question. When you posted it earlier, it was pointed out that you had an equilateral triangle and so it was obvious both what the area was and also where the centre of mass was. It doesn't need double integrals.

May I ask where the question comes from?
4. ahh okay fine..

so its COM is 1/3, 1/3, 1/3 ?

thanks

it is from a double integral problem sheet
5. I think the centroid is (1/3, 1/3, 1/3).

Perhaps they're asking you to practice transforming variables and working out limits in cases that are easy to check by other methods.
6. In which case I assume you're OK with centre-of-mass = first moment of area / area, which I imagine converts into some neat double-integral recipe.

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