📝 Average Value Of A Function And Its Applications

📖 From Calculus • 6. Integration • 20 questions available

Practice MCQs for Average Value Of A Function And Its Applications. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-16

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📝 Sample Questions

Q1. What is the formal definition of the average value of a continuous function \(f\) on the interval \([a,b]\)?

🔹 A. \(\frac{\int_a^b f(x) \, dx}{b-a}\)

🔹 B. \(\int_a^b f(x) \, dx\)

🔹 C. \(\frac{b-a}{\int_a^b f(x) \, dx}\)

🔹 D. \(f(b) - f(a)\)

💡 Difficulty: easy | ✅ Correct: A

Q2. If the average temperature over a day is 68°F and the temperature function is symmetric about noon, which of the following must be true?

🔹 A. The temperature at noon is 68°F

🔹 B. The temperature at 6 am equals the temperature at 6 pm

🔹 C. Both A and B

🔹 D. Neither A nor B

💡 Difficulty: medium | ✅ Correct: C

Q3. In a heat‑transfer problem, the temperature distribution is \(T(x) = 5 - x^2\) on a rod of length 2 m. What is the average temperature along the rod?

🔹 A. 3 °C

🔹 B. 4 °C

🔹 C. 5 °C

🔹 D. 6 °C

💡 Difficulty: hard | ✅ Correct: B

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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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