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Math Help - Area in Polar Coordinates

  1. #1
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    Area in Polar Coordinates

    Find the area of the region which is inside the polar curve :

    r = 3 cos( θ)

    and outside the curve :

    r = 2 − 1 cos( θ)


    Please help!
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  2. #2
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    draw the curves, to see how it looks (looks like a moon)
    then calculate where the curves meet (set r=r, calculate phi1 and phi2, insert phi into the equation and calculate r1 and r2)
    then integrate from r1 to r2 and from phi1 to phi2, using
    area=integral r*dr*dphi

    edit: sorry, my wrong. It's two circles one inside the other, one has radius 3/2 the other 1/2, so the area should be
    pi*(9/4 - 1/4) = pi*2
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  3. #3
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    I still don't understand, what should I integrate and what method should I use to find the area enclosed?
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  4. #4
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    sorry I was wrong with the edit.
    You should start with drawing the curves, to see what you are calculating.
    You draw them first as simple cosine (linear), and then kinda curl them around the middle of the coordinate system.
    Then you calculate the intersection points of the curves.
    Then you can integrate with the intersection points as borders of integration.
    Like this:

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