Find Arc Length of r(t): Solving Homework Problem

megr_ftw
Messages
68
Reaction score
0

Homework Statement


Find the arc length of r(t)= <10sqrt(2), e^10t, e^-10t>, 0 <_ t <_ 1.
<_ is greater than or equal to.


Homework Equations



arc length= integral(magnitude of the derivative of r(t))

The Attempt at a Solution



i thought I figured the answer out and got an arc length of 31149.3, but my online homework is telling me this is the wrong answer. I am not sure what I am doing wrong.
 
Physics news on Phys.org
We can't tell you what you did wrong if we can't see your work. Please show us what you got for r'(t) and |r'(t)|.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top