10.8#3 (edited)

I can not figure out how to solve this problem. I find the derivative of
the vector then set my limits from t=1 to t=2 and then use the formula:

Integral from 1 to 2 sqrt((4^2)+(4x)+(2/x)) and this does not work. What am
I doing wrong?

*************************
You have the limits of integration correct, but it looks like you forgot to square the derivatives of the y and z-components of r.

*********************************
Hello Professor. I've got the steps down to do this problem. I found the upper and lower T values needed, and I have set up the equation. The problem is, I have no clue how to integrate the mess after it is all set up. A clue or step in the right direction would be greatly appreciated!

************************
Well, a good thing to ask yourself might be something like: "Huh. There are very few functions that I've been taught how to integrate. The arc-length formula has the square root of some stuff for an integrand.  What stuff could  be inside that square root that I might reasonably be expected to come up with an anti-derivative for, after taking the square root?"

In fact there are very few things that could be inside the square root that would allow you to do that integral, and if you've done the sum of squares of the components of the derivative correctly when you look at that you see that it turns out to be one of those very few things.