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Math Help - help me with arclength

  1. #1
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    help me with arclength

    Find the arclength of the curve , for .

    I got this: r`(t) = <14t, 2sqrt(7), 1/t> , but I do not know how to integrate it's squareroot.

    Please someone help me...
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  2. #2
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    Quote Originally Posted by zpwnchen View Post
    Find the arclength of the curve , for .


    Please someone help me how to solve it..
    Do you know the formula for arclength when the curve is defined parametrically? Can you differentiate each component with respect to t? Can you substitute the derivatives into the formula and simplify?

    Please show all the working you've been able to do and say where you get stuck.
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  3. #3
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    Yeh i know the arclength formula.

    r \prime (t) = <14t, 2 \sqrt{7}, 1/t>

    arclength L = \int_1^6 \sqrt{(14t)^2+(2 \sqrt{7} )^2 + (1/t)^2}

    Stuck here! dun know how to integrate it
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  4. #4
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    Quote Originally Posted by zpwnchen View Post
    Yeh i know the arclength formula.

    r \prime (t) = <14t, 2 \sqrt{7}, 1/t>

    arclength L = \int_1^6 \sqrt{(14t)^2+(2 \sqrt{7} )^2 + (1/t)^2}

    Stuck here! dun know how to integrate it
    hint ...

    14^2t^2 + 28 + \frac{1}{t^2} = \left(14t + \frac{1}{t}\right)^2 <br />
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  5. #5
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    Gotcha! thank you so much!
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