# Thread: Help with a problem

1. ## Help with a problem

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2. Originally Posted by Marg7
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 ... $t^2+t \ge 0$

$
t(t+1) \ge 0
$

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

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

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

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

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