# Math Help - Arc Length

1. ## Arc Length

Having trouble findin the Arc length of this curve.

x=(1/3)(sqr*(y))(y-3) 4<y<25

I found the first derivative: (sqr*(y)/2 - 1/2sqr*(y)) Is that right?

Then put it into the arclength forumule to set up the integral
sqr*(1+ (sqr*(y)/2 - 1/2sqr*(y))^2)

Now sure how to simplify the terms underneath.

2. Hi

Is it $x = \frac13\:\sqrt{y(y-3)}$ or $x = \frac13\:\sqrt{y}\y-3)" alt="x = \frac13\:\sqrt{y}\y-3)" /> ?

3. The second one ha sorry i wasnt clear (1/3)(sqr*(y)) (y-3)

4. OK $x = \frac13\:\sqrt{y}\y-3)" alt="x = \frac13\:\sqrt{y}\y-3)" />

Hence I agree with your derivative : $\frac{dx}{dy} = \frac{\sqrt{y}}{2} - \frac{1}{2\:\sqrt{y}}$

And

$\sqrt{1+\left(\frac{\sqrt{y}}{2} - \frac{1}{2\:\sqrt{y}}\right)^2} = \frac{\sqrt{y}}{2} + \frac{1}{2\:\sqrt{y}}$

and you're done !