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Math Help - Expressing a Curve in r=r(t) form on an interval I

  1. #1
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    Red face Expressing a Curve in r=r(t) form on an interval I

    The curve is given by y=the integral from 1 to x sqrt[sqrt(t) -1 dt, 1 <=x<=16
    (basically the sqrt sign is over t-1 and the t also has a sqrt over it)
    It asks to express the curve in the form r=r(t) on an Interval I and to find the length of the curve and is the curve smooth
    *I don't understand by which the curve is given...I'm totally lost
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  2. #2
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    Quote Originally Posted by latavee View Post
    The curve is given by y=the integral from 1 to x sqrt[sqrt(t) -1 dt, 1 <=x<=16
    (basically the sqrt sign is over t-1 and the t also has a sqrt over it)
    It asks to express the curve in the form r=r(t) on an Interval I and to find the length of the curve and is the curve smooth
    *I don't understand by which the curve is given...I'm totally lost
    is this what you mean?

    y = \int_1^x \sqrt{\sqrt{t} - 1} \, dt ; 1 \le x \le 16
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  3. #3
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    Yes!

    Yes that's exactly it! Thanks! I was just trying to figure out how to use the symbols
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  4. #4
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    integrate using the substitution u = \sqrt{t} - 1 to find r(t)

    you know how to find arc length?
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  5. #5
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    I know the formula to find the arc length sqrt [1+f'(x)^2]- so do I find the derivative of the function? and where does the [1 to x] factor in?
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  6. #6
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    Quote Originally Posted by latavee View Post
    I know the formula to find the arc length sqrt [1+f'(x)^2]- so do I find the derivative of the function? and where does the [1 to x] factor in?
    familiar with the Fundamental theorem of Calculus ?

    \frac{d}{dx} \left[\int_a^x f(t) \, dt \right] = f(x)
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  7. #7
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    Ok, so the derivative would be:

    y'=sqrt[sqrt(x)-1 corect?
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  8. #8
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    Quote Originally Posted by latavee View Post
    Ok, so the derivative would be:

    y'=sqrt[sqrt(x)-1 corect?
    y' = \sqrt{\sqrt{x}-1} ... correct.
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  9. #9
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    So how would I express that in r(t) form?
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  10. #10
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    as stated in my first response ...

    Quote Originally Posted by skeeter View Post
    integrate using the substitution u = \sqrt{t} - 1 to find r(t)
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  11. #11
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    Ok Thanks!
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