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Transform to polar coordinates

  1. Jun 23, 2008 #1
    Could someone please convert this double integral to polar coordinates?
    0<x<1, x*2<y<1 Int.Int f(x,y)dxdy
  2. jcsd
  3. Jun 23, 2008 #2


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    What is x*2?
  4. Jun 23, 2008 #3
    Sorry x^2
  5. Jun 23, 2008 #4
    If you draw your area, you ll see that it looks like 1/4 of a circle. Use something like that:
    x=1+rcos(fi), y=1+rsin(fi). R will be going from 0 to 1, fi from -pi/2 to 0 then. dxdy gets changed to rdrdfi.
    This is not the only solution of course.
  6. Jun 23, 2008 #5


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    (have an int: ∫ and a squared: ² and a theta: θ and a pi: π :smile:)

    The area is a triangle for π/4 < θ < π/2.

    For 0 < θ < π/4, you simply need to write the boundary as an equation in r and θ.

    Hint: for 0 < θ < π/4, each line of constant θ has tanθ = y/x, and it hits the boundary at y = x².

    So what is the value of x at the boundary … and what value of r does that correspond to? :smile:
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