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Math Help - Complicated Curve Length

  1. #1
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    Complicated Curve Length

    Compute the length of the parametric curve
    x=(t2−2)sint+2tcost
    y=(2−t2)cost+2tsint




    from t1=0 to t2=

    I know that I need to square the derivatives, and then add them together, and square root them, and then integrate. Is there anyway to uncomplicate the terms before I start doing the derivative? As it stands, it looks like it will be unnecessarily complicated...
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  2. #2
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    Quote Originally Posted by Hellreaver View Post
    Compute the length of the parametric curve
    x=(t2−2)sint+2tcost
    y=(2−t2)cost+2tsint




    from t1=0 to t2=

    I know that I need to square the derivatives, and then add them together, and square root them, and then integrate. Is there anyway to uncomplicate the terms before I start doing the derivative? As it stands, it looks like it will be unnecessarily complicated...
    If you take the two derivatives, square them and add (and simplify) you should end up with

    x_t^2 + y_t^2 = t^4
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    AH! Sorry, I copied the question down wrong...

    Compute the length of the parametric curve
    x=(t^2−2)sint+2t cost
    y=(2−t^2)cost+2t sint

    I don't know if that changes anything. Sorry again, I was in a hurry as I needed to get a 2000 word english essay done...
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  4. #4
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    Quote Originally Posted by Hellreaver View Post
    Compute the length of the parametric curve
    x=(t2−2)sint+2tcost
    y=(2−t2)cost+2tsint
    With your original post, the placing of the two in t2 suggested that it was t^2 and that's what I assumed (I know assuming is bad). So my answer is still good.
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    Ok awesome. Thanks so much. I just had to check, because it was a dumb mistake on my part.
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