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Double integral, find area

  1. Aug 26, 2013 #1
    "Hey guys, how are you? I was studying for my calculus final and stumbled upon a peculiar function.

    1. The problem statement, all variables and given/known data

    Now I have to find the area bounded by the function (x^2+y^2)^3=xy^4 using a double integral. Now, the problem is that the graph is totally unknown to me (I have some ideas but im not shure).

    2. Relevant equations

    (x^2+y^2)^3=xy^4

    3. The attempt at a solution

    A substitution with u and v, doesnt seem to work and going to polar doesnt work either :/ Maybe Im doing something wrong, I dont know. Can anybody help me? Thank you in advance :)
     
  2. jcsd
  3. Aug 26, 2013 #2
    Use polar coordinates.
     
  4. Aug 26, 2013 #3
    It doesnt seem to solve that way. Can you please write just the polar equation in this case?
     
  5. Aug 26, 2013 #4

    Ray Vickson

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    Just as a matter of terminology: you do not have a "function; you have two functions and one equation connecting them (to form a curve). At first I had a lot of trouble trying to decipher your post.

    Certainly, a judicious change of variables makes the problem pretty straightforward.
     
  6. Aug 26, 2013 #5
    Two functions? Yes, but can the whole equation be plotted using the sepparate functions? Im sorry, but I really need to imagine the area of integration. And as for the change of variables, I was thinking u = x^2 + y^2, ok, but then?
     
  7. Aug 29, 2013 #6
    I am attempting to do this problem, quick question just for clarity: is it x*y^4 of (x*y)^4?
     
  8. Aug 29, 2013 #7

    Zondrina

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    It is read ##x*y^4##.

    As for the problem, a simple change to polar co-ordinates is all that is needed.
     
  9. Sep 10, 2013 #8
    Thank you everyone :)
     
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