📝 The Mean Value Theorem for Integrals

Q1. If the average value of a continuous function \(f\) on \([2,5]\) is 7, what is \(\int_2^5 f(x) \, dx\)?

💡 Difficulty: easy | ✅ Correct: C

Q2. Consider \(f(x) = e^x\) on \([0,1]\). Which of the following statements is true regarding the point \(c\) guaranteed by the theorem?

💡 Difficulty: medium | ✅ Correct: D

Q3. A particle moves along a line with position \(s(t) = t^3 - 6t^2 + 9t\) on \([0,3]\). Using the theorem, which statement about its average velocity is correct?

💡 Difficulty: hard | ✅ Correct: A