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📝 Arc Length

📖 From Calculus • 7. Applications of the Definite Integral In Geometry, Science, and Engineering • 23 questions available

Practice MCQs for Arc Length. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-16

6
Easy Questions
11
Medium Questions
6
Hard Questions

📝 Sample Questions

Q1. Find the length of the curve \(y=x^{2}\) on the interval \([0,1]\).

🔹 A. \(L=\frac{\sqrt{5}}{2}+\frac{1}{4}\ln\!\left(\frac{\sqrt{5}+1}{\sqrt{5}-1}\right)\)
🔹 B. \(L\approx1.478\)
🔹 C. \(L\approx1.317\)
🔹 D. \(L\approx1.618\)

💡 Difficulty: easy | ✅ Correct: A

Q2. A road is modeled by \(y=0.1x^{2}\) (with \(x\) in kilometers). Find the road length from \(x=0\) to \(x=5\) km.

🔹 A. \(5.02\) km
🔹 B. \(5.12\) km
🔹 C. \(5.31\) km
🔹 D. \(5.45\) km

💡 Difficulty: medium | ✅ Correct: B

Q3. Determine the length of the polar curve \(r=e^{\theta}\) from \(\theta=0\) to \(\theta=\ln 2\).

🔹 A. \(2\)
🔹 B. \(3\)
🔹 C. \( \sqrt{5}\)
🔹 D. \( \sqrt{10}\)

💡 Difficulty: hard | ✅ Correct: C

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🔗 Related Topics

📝 Approximating Roots📝 Areas and Limits📝 Continuity in Applications📝 Continuity of Compositions📝 Continuity of Inverse Functions
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