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Cylindrical to rectangular coordinates

  1. Nov 6, 2011 #1
    Hi sorry,I still need some help on converting coordinates >.<

    Set up an integral in rectangular coordinates equivalent to the integral

    ∫([itex]0 ≤ θ ≤ \frac{∏}{2})[/itex]∫([itex]1 ≤ r ≤ \sqrt{3})[/itex]∫(1 ≤ z ≤ √(4-r2)) r3(sinθcosθ)z2 dz dr dθ

    Arrange the order of integration to be z first,then y,then x.

    I manage to convert,however the answer has 2 parts and I only managed to get 1 part.How do I know if the answer will have more than 1 part?

    thanks in advance!
  2. jcsd
  3. Nov 6, 2011 #2

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    Hi again violette! :smile:

    What did you convert?
    What are parts 1 and 2?
    Did you already try to make a drawing?
  4. Nov 6, 2011 #3
    Hi I like Serena,really thanks so much for being so helpful =D

    hmm...how do I draw with cylindrical coordinates?I only know how to make a drawing given rectangular coords >.<

    this was what I got:
    ∫(0 ≤ z ≤ 1)∫(√(1-x2) ≤ y ≤ √(3-x2)∫(1 ≤ x ≤ √(4-x2-y2) z2xy dzdydx
  5. Nov 6, 2011 #4

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    Well, you draw in rectangular coordinates, but you add circles for constant r.

    Here's an example:

    But that's looking good! :smile:

    You only seem to have switched x and z around in the limits or something.
    And the limits (0 ≤ ° ≤ 1) are not right.

    How did you get that?
  6. Nov 6, 2011 #5
    omg thanks so much!The diagram made it easier for me to try on my own =)

    Ah oopx,it should be this:
    ∫(0 ≤ x ≤ 1)∫(√(1-x2) ≤ y ≤ √(3-x2)∫(1 ≤ z ≤ √(4-x2-y2) z2xy dzdydx

    Hmm,actually I got 3 values for x after all the conversion: 0,1 and [itex]\sqrt{3}[/itex].
    But I used 0 and 1 because they are the limits that fitted y
  7. Nov 6, 2011 #6

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    Yes, that's basically it.
    The upper limit for x is still [itex]\sqrt{3}[/itex]. You cannot just discard that part of the object.
    However, the lower limit for y needs to be modified to 0 if it would otherwise be undefined.
    In your diagram you should be able to see why that is.

    You can write that for instance like √max(0, 1-x2) ≤ y ≤ √(3-x2).
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