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Thread: Help with a problem

  1. #1
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    Help with a problem

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    Last edited by Marg7; Feb 22nd 2010 at 01:58 PM.
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  2. #2
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    Quote Originally Posted by Marg7 View Post
    Let F(x)= ∫sqrt(t^2 + t) dt (from 1 to 2x)

    Find: -the domain of F(x)

    -the limit of F(x) as x approaches 1/2

    -the length of the curve y=F(x) for x is greater than or equal to 1 and less than or equal to 2

    How would I go about doing these? Thank you!
    domain ... $\displaystyle t^2+t \ge 0$

    $\displaystyle
    t(t+1) \ge 0
    $

    either $\displaystyle t \le -1$ , or $\displaystyle t \ge 0$

    since the lower limit is $\displaystyle x = 1$ , $\displaystyle 2x \ge 0$ ... $\displaystyle x \ge 0$


    $\displaystyle
    \lim_{x \to \frac{1}{2}} F(x) = 0
    $



    $\displaystyle
    S = \int_1^2 \sqrt{1 + [F'(x)]^2} \, dx
    $

    where $\displaystyle F'(x) = 2\sqrt{4x^2 + 2x}$
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