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Another Polar Coordinates + Integration Question

  1. Sep 24, 2009 #1
    I came across this example on the net :

    We are integrating over the region that is the area inside of r = 3 + 2 sin θ and outside of r = 2, working in polar coordinates (r,θ).

    What is the limits of integration for θ?


    # I already know the answer. But I have no idea how to arrive at the solution.

    # Do I sketch r = 3 + 2 sin θ and r = 2? r = 2 is just circle centered at origin with radius 2. What about r = 3 + 2 sin θ?
     
  2. jcsd
  3. Sep 24, 2009 #2

    LCKurtz

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    Yes, you should plot them. The curves cross where they have equal r values. Set the r's equal and solve for theta. Then, using your picture to see which region is being asked for, set up an integral like this:

    [tex]A = \int_{\theta_0}^{\theta_1} \int_{r_{inner}}^{r_{outer}} r dr d\theta[/tex]

    Check your picture and be sure you are integrating in the positive direction for theta.
     
  4. Sep 24, 2009 #3
    How do I plot r = 3 + 2 sin θ without resorting to a graphing calculator? (and without knowing that equation represents a Limaçon)
     
  5. Sep 24, 2009 #4
    Help! I just got to this site because i am looking for help with wind generators but can't figure out how to start a new thead.

    can you help or direct me to where I need to go?
     
  6. Sep 24, 2009 #5

    LCKurtz

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    Make a table of values. For every 30 degrees (pi/6) value of theta plot r.
     
  7. Sep 24, 2009 #6

    LCKurtz

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    At the top of the page click on Physics Forums. Then click on one that looks good for that topic. Then click on the "New Topic" button there at the top.
     
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