Number 
Question 
Answer 
See the work 
1. 
Find the arclength of the curve
, for
1 &le t &le 9.
L = 
L = 562.197 
The work 
2. 
Find the length of the given curve:
r(t) = ( 5t, 4sin(t), 4cos(t) )
where 5 &le t &le 2.

r(t) = 44.822 
The work 
3. 
Find the arclength of the curve
,
0 &le t &le 1

22026.466 
The work 
4. 
Consider the path
defined for t > 0.
Find the length of the curve between the points
(6, 3, 0) and ( 30, 75, 3ln(5) ).

76.828 
The work 
5. 
Consider the curve
.
Compute the arclength function s(t): (with initial point t=0).


The work 
6. 
Starting from the point ( 1, 5, 3 ), reparametrize
the curve
r(t) = ( 1  t, 5  2t, 3  t ) in terms of
arclength.
r(t(s)) = (,
,) 

The work 
7. 
Starting from the point ( 1, 2, 4 )
reparametrize the curve
r(t) = ( 1 + t) i + ( 2 + 2t) j + ( 4  2t ) k
in terms of arclength.
r(t(s)) = i +
j + k 
1 + s/3i + 2 + 2s/3j + 4  2s/3k

The work 
