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Math Help - Parametric Equation

  1. #1
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    Parametric Equation

    I have a question that I am working on and am having difficulties knowing how to approach it. 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?
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  2. #2
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    I know how to do PART A I am having difficulties with part B finding the area!

    Part A:

    -5/6 t + 5t + 1 = -5/6 [-t] + 5[-t] + 1
    -5/6 t + 5t = 0
    t - 6t = 0
    t = 0
    t = +/-√6


    For the Area

    S = integral of y dx
    S = integral of [-5/6 t + 5t + 1] d[6 - 5/2 t]
    S = integral of [-5/6 t + 5t + 1] 5tdt from T+ to T-
    But I am not getting the right answer... Can anyone help?
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  3. #3
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    Hello, SmileyFace143!

    Just what is the right answer?
    Give us something to aim at . . .


    t = \pm\sqrt{6}

    A \;=\;\int^b_a y\,dx

    We have: . A \;=\;\int^{\sqrt{6}}_{\text{-}\sqrt{6}}\left[-\frac{5}{6}t^3 + 5t + 1\right]\bigg[-5t\,dt\bigg] \;=\;\int^{\sqrt{6}}_{\text{-}\sqrt{6}}\left[\frac{25}{6}t^4 - 25t^2 - 5t\right]\,dt

    But I'm getting a negative answer . . .

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  4. #4
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    There isnt a given answer. It is an online submission that just says right or wrong, with an unlimited number of tries. I have gotten the answer you came up with too -29 and it isnt correct so I am not too sure what I am doing wrong.
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