1. help me with arclength

Find the arclength of the curve , for .

I got this: r`(t) = <14t, 2sqrt(7), 1/t> , but I do not know how to integrate it's squareroot.

2. Originally Posted by zpwnchen
Find the arclength of the curve , for .

Please someone help me how to solve it..
Do you know the formula for arclength when the curve is defined parametrically? Can you differentiate each component with respect to t? Can you substitute the derivatives into the formula and simplify?

Please show all the working you've been able to do and say where you get stuck.

3. Yeh i know the arclength formula.

$\displaystyle r \prime (t) = <14t, 2 \sqrt{7}, 1/t>$

arclength L = $\displaystyle \int_1^6 \sqrt{(14t)^2+(2 \sqrt{7} )^2 + (1/t)^2}$

Stuck here! dun know how to integrate it

4. Originally Posted by zpwnchen
Yeh i know the arclength formula.

$\displaystyle r \prime (t) = <14t, 2 \sqrt{7}, 1/t>$

arclength L = $\displaystyle \int_1^6 \sqrt{(14t)^2+(2 \sqrt{7} )^2 + (1/t)^2}$

Stuck here! dun know how to integrate it
hint ...

$\displaystyle 14^2t^2 + 28 + \frac{1}{t^2} = \left(14t + \frac{1}{t}\right)^2$

5. Gotcha! thank you so much!