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Homework Help: Double Integral Polar

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  1. Dec 1, 2017 #1
    1. The problem statement, all variables and given/known data
    r=1 and r=1+cos(theta), use a double integral to find the area inside the circle r=1 and outside the cardioid r=1+cos(theta)

    2. Relevant equations


    3. The attempt at a solution
    I am confused on the wording and how to set it up. I tried setting it up by setting theta 0 to pi. and r as 1 to 1+cos(theta). I used r drd(theta) as the equation to use.
     
  2. jcsd
  3. Dec 1, 2017 #2

    BvU

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    Make a picture !
    upload_2017-12-1_18-21-19.png
     
  4. Dec 1, 2017 #3
    I did make a picture I am confused by the little piece of the cardoid that isn't in the first quadrant.
     
  5. Dec 1, 2017 #4

    Ray Vickson

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    In the whole plane, what is the region outside the cardioid? What is the region inside the circle? What is the intersection of those two regions?
     
    Last edited: Dec 1, 2017
  6. Dec 2, 2017 #5

    Mark44

    Staff: Mentor

    As shown in BvU's graph, the region of integration is entirely on the left side of the vertical axis. What is ##\theta## at the upper intersection point? At the lower intersection point? There is also some symmetry you can take advantage of.
     
  7. Dec 3, 2017 #6

    BvU

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    Ambiguous -- in the picture a small piece is missing because I simply didn't grab the full ##\theta## range for the red curve :smile:
     
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