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Having trouble with double integrals in polar coordinates?

  1. Nov 17, 2011 #1
    I'm having trouble figuring out how to find what "r" is. I know r is the radius, but how do I go about finding it? Like what do I look for in a particular problem?
     
  2. jcsd
  3. Nov 17, 2011 #2
    Maybe if you gave the equation you'd get something more definite. But for polar coordinates what i'd do personally is convert it to a set of parametric equations and integrate those separately with respect to the parameter.

    R is usually given by a polar equation, i'm not quite sure what you're asking.
     
    Last edited: Nov 17, 2011
  4. Nov 17, 2011 #3
    @gordonj005: I mean I'm confused as to what steps to take to find the radius, r.
     
  5. Nov 17, 2011 #4
    again it would be helpful if you gave the context. the radius is just the distance from the origin. where do the double integrals fit in?
     
  6. Nov 17, 2011 #5
    Okay here is a problem from my homework, and I'm stuck on finding the lower bound for r:

    Graph r=1/(9cos(t)) for -∏/2≤t≤∏/2 and r=1. Then write an iterated integral in polar coordinates representing the area inside the curve r=1 and to the right of r=1/(9cost) . (Use t for theta in your work.)

    I got the bounds for t -arccos(1/9) ≤t≤ arccos(1/9) and I have the upper bound for r to be 1, but I can't get the lower bound, any ideas?

    Thank you
     
  7. Nov 17, 2011 #6
    sorry, just to clarify.. [itex] r = \frac{1}{9 \cos{t}}[/itex] for [itex]-\pi \le t \le \frac{\pi}{2}[/itex] and [itex] r = 1 [/itex] right?

    For the lower bound on r, I believe it is [itex]\frac{-1}{9} [/itex], but i'm not entirely sure about that, maybe someone else can look at this.

    In terms of the iterated integral here's a few tips:
    [tex] x = r \cos{t} [/tex]
    [tex] y = r \sin{t} [/tex]
    [tex] dA = r dr dt [/tex]

    and you're integrating a function of the form [itex] f(x, y) [/itex].
     
  8. Nov 23, 2011 #7
    would you mind? can you please ans this.... please find the polar form of 1/4i also the 1/z? please
     
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