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Thread: Area and Parametric Equations

  1. #1
    Mar 2008

    Area and Parametric Equations

    I have a question that I am working on and am having difficulties with part B finding the area. It looks like this:

    The following parametric equations trace out a loop.
    x = 6 - (5/2)t^2
    y = (-5/6)t^3+5t+1

    A)Find the t values at which the curve intersects itself:
    t= +/- ______
    b) What is the total area inside the loop?

    For A my values are t= +/- Sqrt(6)

    For the Area I had this
    The integral from sqrt(6) to -Sqrt(6) = (25/6)t^4-25t^2-5t
    When integrated = (25/6)(t^5/5)-25(t^3/3)-5(t^2/2) evaluated at sqrt(6) and (-sqrt6) this yeilds a negative answer and is not correct. CAN ANYONE HELP??
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Feb 2008
    Yuma, AZ, USA

    Green's Theorem

    If C is a positively oreinted simple closed curve then the area enclosed by it is given by

    $\displaystyle A=\oint_{C}xdy =-\oint_{C}ydx=\frac{1}{2}\oint_{C}xdy-ydx$

    I think you forgot the minus sign in $\displaystyle -\oint_{C}ydx$

    P.S. The value I get is $\displaystyle 40\sqrt{6}$
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