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Thread: finding lengths of curves

  1. November 26th 2010, 04:12 AM #1
    berto
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    finding lengths of curves

    simple question of two problems that are alike

    1
    the interval is 5 ≤ x ≤ 7, the function is y = [(x^4)/4] + [1/(8x^2)]

    here, i just integrate function from 5 to 7, correct?


    2
    the interval is 1≤ x ≤ 9, but i am given an integral from one to x of √[(t^3) - 1]dx

    i just replace x with 9 and evaluate, correct?

    forgive english please! thank you
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  2. November 26th 2010, 05:33 AM #2
    DrSteve
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    To compute arc length you must integrate 1+(\frac{dy}{dx})^2 over the indicated interval.
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  3. November 26th 2010, 05:36 AM #3
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    Quote Originally Posted by DrSteve View Post
    To compute arc length you must integrate 1+(\frac{dy}{dx})^2 over the indicated interval.
    Actually, it's \displaystyle \sqrt{1 + \left(\frac{dy}{dx}\right)^2} that you need to integrate.
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  4. November 26th 2010, 05:36 AM #4
    skeeter
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    \displaystyle S = \int_a^b \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx
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  5. November 26th 2010, 06:41 AM #5
    DrSteve
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    Yep - I accidentally left off the square root - sorry about that.
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