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Double intergral

  1. Dec 9, 2011 #1
    1. The problem statement, all variables and given/known data
    Consider the heat density function for a metal plate: x + y2 + x2

    Find the total heat in the plate given that the plate resides in the region x≥0, y≥0, x2 + y2 ≥ 1


    3. The attempt at a solution

    i thought it was pretty straightforward. i did a double integral with both limits being 0 to 1 but my professor said the y limit is not to 1. what is the top limit then?
     
  2. jcsd
  3. Dec 9, 2011 #2

    ehild

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    Are you sure you copied the last formula correctly? I would mean both x and y going to infinity.

    ehild
     
  4. Dec 9, 2011 #3
    should be less than or equal to 1
     
  5. Dec 9, 2011 #4
    so is the upper limit of y just sqrt(1-x^2) ?
     
  6. Dec 9, 2011 #5
    Correct
     
  7. Dec 9, 2011 #6
    ok now i cant do the integral..


    first step, integrate WRT y. so the function becomes x + (y^3)/3 + x^2
    plugging the limits for y in:

    [x + [ (1-x^2)^(3/2) / 3 ] + x^2] - x - 0 - x^2

    so youre just left with [ (1-x^2)^(3/2) / 3 ]. how do you integrate that WRT x ??
     
    Last edited: Dec 9, 2011
  8. Dec 9, 2011 #7

    HallsofIvy

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    Let [itex]x= sin(\theta)[/itex]. That's a pretty standard integral.
     
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