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Math Help - Help with a problem

  1. #1
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    Help with a problem

    [/I]
    Last edited by Marg7; February 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 ... t^2+t \ge 0

     <br />
t(t+1) \ge 0<br />

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

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


     <br />
\lim_{x \to \frac{1}{2}} F(x) = 0<br />



     <br />
S = \int_1^2 \sqrt{1 + [F'(x)]^2} \, dx<br />

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