Calculating Arc Length in Multivariate Calculus

[crazynut52]

here is the problem, and I can't seem to get very far,

compute the length of r(t) = <3t, 4cost, 4sint> from t=0 to t=1

i know the formula is integral from 0 to 1 of length of r'(t)

but I keep coming up with 5, and it doesn't seem right, can someone please confirm or deny this. Thanks

 

[tink]

that seems to be what i get too. r'(t) = 5, so when you integrate this from 0 to 1 it gives you 5 again.

 

[robphy]

If you look at what you've plotted, i believe it is the hypotenuse of a right triangle with base 4 and height 3 wrapped around a cylinder [of radius 4].