Calculating Arc Length in Multivariate Calculus

AI Thread Summary
To compute the arc length of the vector function r(t) = <3t, 4cost, 4sint> from t=0 to t=1, the correct approach involves finding r'(t) and integrating its magnitude. The derivative r'(t) is calculated to be a constant value of 5. When integrating this constant from 0 to 1, the result is indeed 5, confirming the arc length. The discussion highlights that the plotted curve represents the hypotenuse of a right triangle with a base of 4 and a height of 3, suggesting a cylindrical shape. The conclusion affirms that the calculated arc length of 5 is accurate.
crazynut52
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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
 
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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.
 
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].
 

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