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Math Help - Areas of cardioids

  1. #1
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    Exclamation Areas of cardioids

    How can I determine the bounds of integral which we use while calculating carsioids. For example: find the area shared by r=2(1+sinθ) and r=2 ??
    Last edited by mr fantastic; January 6th 2010 at 08:47 PM. Reason: Removed shouting
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by fromTURKEY View Post
    HOW CAN I DETERMINE THE BOUNDS OF INTEGRAL WHICH WE USE WHILE CALCULATING CARDIOIDS.FOR EXAMPLE: FIND THE AREA SHARED BY r=2(1+sinθ) and r=2 ??
    There is a formula for this you know? Have you tried to graph the two curves to find the bounds for integration?

    2=2\left(1+\sin(\theta)\right)\implies 1+\sin(\theta)=1\implies \sin(\theta)=0
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    But, is it one of bounds or will we find the bounds after that ?
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by fromTURKEY View Post
    But, is it one of bounds or will we find the bounds after that ?
    ....how may solutions are there to \sin\left(\theta\right)=0?
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  5. #5
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    two ! 0 and π. but according to my book, bounds are 0 and π/2
    the other bounds are -π/2 and 0 ?? help me please. I have a final exam tomarrow..
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  6. #6
    MHF Contributor Calculus26's Avatar
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    For the shared area once you have 0 and pi as Drexel pinted out -note from 0 to pi you simply have the area of a half circle and from pi to 2pi you have the area inside the cardioid obtained by doubling the integral of

    2(1+sin(t)) from pi to 3pi/2.

    See graph in attachment
    Attached Thumbnails Attached Thumbnails Areas of cardioids-cardioid.jpg  
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  7. #7
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    No, I did not understand..How did we determine the bounds as from pi to 3pi/2
    Last edited by mr fantastic; January 6th 2010 at 08:48 PM. Reason: Removed shouting
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  8. #8
    MHF Contributor Calculus26's Avatar
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    Ok--- for the area inside the cardioid it should be fairly obvious you could integrate from pi to 2pi.

    Now just split that interval in two.
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