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Homework Help: Change to polars double integral

  1. Dec 16, 2011 #1
    1. The problem statement, all variables and given/known data

    Here is the question


    2. Relevant equations

    3. The attempt at a solution

    So converting to polars by x = r cos θ, y = r sin θ gives me r^5 in the inner integral

    but how do you convert the ranges?

    y goes from 0 to sqrt 1 - x^2, so that is just r, I could tell just by looking at it, but in a harder question how do you derive the range in terms of r? x goes from 0 to 1, but how do you convert that in terms of θ (an angle)?
  2. jcsd
  3. Dec 16, 2011 #2


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    Have you sketched the region of integration?
  4. Dec 16, 2011 #3


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    Draw the domain of integration in the x,y plane (like in the figure) and find the ranges of θ and r from there.


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