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Finding the total mass?

  1. Aug 20, 2012 #1
    1. The problem statement, all variables and given/known data
    Let the surface S be the part of the plane 2x-y+z=3 that lies above the triangle in the xy plane that is bounded by the lines y=0, x=1 and y=x. Find the total mass of S if its density (mass per unit area) is given by

    ρ(x,y,z)= xy+z


    2. Relevant equations



    3. The attempt at a solution

    Ok so i know this is a double integral. the limite will be
    0≤x≤1
    0≤y≤2x-3

    and f'(x)= 2, f'(y)= -1

    √(f'(x) + f'(y) + 1)= √6

    so my equation is

    √6∫∫(xy+z)

    and i have a feeling im meant to convert this into polar coordinates but how do you convert the limits to polar coordinates?
     
  2. jcsd
  3. Aug 20, 2012 #2
    You don't need any polar coordinates here. You simply need to express z via x and y in the integral you have got so far. And by the way, it is a mistake not to write dxdy in the integral.
     
  4. Aug 20, 2012 #3
    A volume integral seems to yield an easy result here.
     
  5. Aug 23, 2012 #4
    thanks heaps guys, i figured it out, and sorry about the late reply
     
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