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Math Help - Equation for a Curve

  1. #1
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    Equation for a Curve

    The length of a curve from x=1 to x=4 is given by
    If the curve contains the point (1,6), what's the equation of the curve?

    (Sorry, ignore the second part of that picture...it came with the plain integral part because I copied from Wolfram)
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  2. #2
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    Quote Originally Posted by BeiW View Post
    The length of a curve from x=1 to x=4 is given by
    If the curve contains the point (1,6), what's the equation of the curve?

    (Sorry, ignore the second part of that picture...it came with the plain integral part because I copied from Wolfram)
    arc length ...

    S = \int_a^b \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx

    for your problem ...

    \frac{dy}{dx} = \pm 3x^2

    y = \pm x^3 + C

    6 = \pm 1^3 + C

    C = 5 or C = 7

    two possible functions ...

    y = x^3 + 5

    y = 7 - x^3
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  3. #3
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    awesome, thanks!
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