1
Arc Length- HW Problems
Find the length of the following curves.
1. 𝑐⃗(𝑡) =< 4 cos(𝑡) , 4 sin(𝑡) , 3𝑡 >; 0 ≤ 𝑡 ≤ 2𝜋
4 3
2. 𝑐⃗(𝑡) =< cos(𝑡) , 1 − sin(𝑡) , − cos(𝑡) >; 3≤𝑡≤6
5 5
2 3
3. 𝑐⃗(𝑡) =< sin(𝑡) , cos(𝑡) , 𝑡 2 >; 0≤𝑡≤8
3
4. 𝑐⃗(𝑡) =< 2𝑡 + 1, ln(𝑡) , 𝑡 2 − 1 >; between (3,0,0) and
(5, ln(2) , 3).
1
5. 𝑐⃗(𝑡) =< 𝑡 3 , 𝑡 2 , 𝑡 2 >; 0≤𝑡≤2
3
√2 √2
6. 𝑐⃗(𝑡) =< cosh(𝑡) , 𝑡, 𝑡 >; 0 ≤ 𝑡 ≤ ln(3)
2 2
Arc Length- HW Problems
Find the length of the following curves.
1. 𝑐⃗(𝑡) =< 4 cos(𝑡) , 4 sin(𝑡) , 3𝑡 >; 0 ≤ 𝑡 ≤ 2𝜋
4 3
2. 𝑐⃗(𝑡) =< cos(𝑡) , 1 − sin(𝑡) , − cos(𝑡) >; 3≤𝑡≤6
5 5
2 3
3. 𝑐⃗(𝑡) =< sin(𝑡) , cos(𝑡) , 𝑡 2 >; 0≤𝑡≤8
3
4. 𝑐⃗(𝑡) =< 2𝑡 + 1, ln(𝑡) , 𝑡 2 − 1 >; between (3,0,0) and
(5, ln(2) , 3).
1
5. 𝑐⃗(𝑡) =< 𝑡 3 , 𝑡 2 , 𝑡 2 >; 0≤𝑡≤2
3
√2 √2
6. 𝑐⃗(𝑡) =< cosh(𝑡) , 𝑡, 𝑡 >; 0 ≤ 𝑡 ≤ ln(3)
2 2
