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Math Help - Arc Lengths

  1. #1
    Junior Member superman69's Avatar
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    Arc Lengths

    Find the length of the curve defined by from to .

    Ok so first I know that we have to take the derivative which is Arc Lengths-msp50519805hecidbcbe5i00001d120773aec0a4a1.gif And What would I do from then?
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  2. #2
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    Quote Originally Posted by superman69 View Post
    Find the length of the curve defined by from to .

    Ok so first I know that we have to take the derivative which is Click image for larger version. 

Name:	MSP50519805hecidbcbe5i00001d120773aec0a4a1.gif 
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ID:	13472 And What would I do from then?
    There are numerical errors in your derivative. After you have fixed them you should simplify the result, substitute it into the arclength formula (which I assume you have been taught) and then do the resulting integration.
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  3. #3
    Junior Member superman69's Avatar
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    Quote Originally Posted by mr fantastic View Post
    There are numerical errors in your derivative. After you have fixed them you should simplify the result, substitute it into the arclength formula (which I assume you have been taught) and then do the resulting integration.
    Yes. But is this how you would set the equation Arc Lengths-msp46719805i312gi7i58d00000i697g989f0fhgc3.gif
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  4. #4
    Junior Member superman69's Avatar
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    Oh I see the mistake, 9 were suppose to be a 4
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  5. #5
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    Quote Originally Posted by superman69 View Post
    Yes. But is this how you would set the equation Click image for larger version. 

Name:	MSP46719805i312gi7i58d00000i697g989f0fhgc3.gif 
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    Once you have made the necessary correction, the thing you are square rooting will simplify to \left(\frac{x^2 + 16}{x^2 - 16}\right)^2.
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  6. #6
    Junior Member superman69's Avatar
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    Quote Originally Posted by The Second Solution View Post
    Once you have made the necessary correction, the thing you are square rooting will simplify to \left(\frac{x^2 + 16}{x^2 - 16}\right)^2.

    So this was what I got so far but I don't seem sure if this is correct
    Arc Lengths-msp4941980625i14hbcc1b000016374e8ec418b9af.gif
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  7. #7
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    Quote Originally Posted by superman69 View Post
    So this was what I got so far but I don't seem sure if this is correct
    Click image for larger version. 

Name:	MSP4941980625i14hbcc1b000016374e8ec418b9af.gif 
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ID:	13474
    Look, you need to get the derivative correct first. Please post your simplified answer for it and show all your working for how you got it.

    Then ..... post #5 tells you what the 1 + \left( \frac{dy}{dx}\right)^2 will simplify to.
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