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Math Help - Arc Length

  1. #1
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    Arc Length

    Find the length of the curve y= (x^2/2) - (ln x / 4) from x = 2 to x = 4.

    My attempt:

    y' = x- (1/4x)

    length = Int 2 - 4 root ( (1 + (x- (1/4x))^2)) dx

    = Int 2 - 4 root (1+ x - 1/2 + 1/16x^2) dx


    I cant work this out. Is it because I did this part wrong, or just because I can't figure out the integral?
    Last edited by veronicak5678; October 5th 2008 at 07:58 AM.
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  2. #2
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    y = \frac{x^2}{2} - \frac{\ln{x}}{4}

    y' = x - \frac{1}{4x}

    (y')^2 = x^2 - \frac{1}{2} + \frac{1}{16x^2}

    S = \int_2^4 \sqrt{1 + \left(x^2 - \frac{1}{2} + \frac{1}{16x^2}\right)} \, dx

    S = \int_2^4 \sqrt{x^2 + \frac{1}{2} + \frac{1}{16x^2}} \, dx

    S = \int_2^4 \sqrt{\left(x + \frac{1}{4x}\right)^2} \, dx

    S = \int_2^4 \left(x + \frac{1}{4x}\right) \, dx

    can you finish?
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  3. #3
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    I see. I would never have thought to do that. Thanks again.
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