1
Arc Length- HW Problems
Find the length of the following curves.
2 3
1. 𝑦 = 2 + 𝑥2 ; 0≤𝑥≤3
3
𝑥3 1
2. 𝑦 =
3
+ 4𝑥 ; 1≤𝑥≤3
𝑦4 1
3. 𝑥 =
8
+ 4𝑦2 ; 1≤𝑦≤2
𝜋 3𝜋
4. 𝑦 = ln[𝑠𝑖𝑛(𝑥 )] ; ≤𝑥≤
4 4
𝑒𝑥 +𝑒−𝑥
5. 𝑦 = ; 0≤𝑥≤2
2
3 2
6. 𝑥 =
2
𝑦3 +1; 1 ≤ 𝑦 ≤ 27
1 3 1
7. 𝑦 =
3
𝑥2 −𝑥 ; 2 1≤𝑥≤4
8. Use Simpson’s rule with 𝑛 = 10 to approximate the length of
𝑦 = 𝑥𝑠𝑖𝑛(𝑥 ) ; 0 ≤ 𝑥 ≤ 𝜋.
Arc Length- HW Problems
Find the length of the following curves.
2 3
1. 𝑦 = 2 + 𝑥2 ; 0≤𝑥≤3
3
𝑥3 1
2. 𝑦 =
3
+ 4𝑥 ; 1≤𝑥≤3
𝑦4 1
3. 𝑥 =
8
+ 4𝑦2 ; 1≤𝑦≤2
𝜋 3𝜋
4. 𝑦 = ln[𝑠𝑖𝑛(𝑥 )] ; ≤𝑥≤
4 4
𝑒𝑥 +𝑒−𝑥
5. 𝑦 = ; 0≤𝑥≤2
2
3 2
6. 𝑥 =
2
𝑦3 +1; 1 ≤ 𝑦 ≤ 27
1 3 1
7. 𝑦 =
3
𝑥2 −𝑥 ; 2 1≤𝑥≤4
8. Use Simpson’s rule with 𝑛 = 10 to approximate the length of
𝑦 = 𝑥𝑠𝑖𝑛(𝑥 ) ; 0 ≤ 𝑥 ≤ 𝜋.
