📝 Changing The Limits Of Summation

📖 From Calculus • 6. Integration • 18 questions available

Practice MCQs for Changing The Limits Of Summation. 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. A dragster's velocity \(v(t)\) is given in m/s for \(0 \le t \le 5\). To find total distance, which expression correctly changes the summation limit to an integral?

🔹 A. \(\sum_{i=1}^{5} v(i) \Delta t\)

🔹 B. \(\int_{0}^{5} v(t) \, dt\)

🔹 C. \(\sum_{i=0}^{5} v(i)\)

🔹 D. \(\int_{5}^{0} v(t) \, dt\)

💡 Difficulty: easy | ✅ Correct: B

Q2. A rectangular region has width \(w(t) = 2t\) and height \(h(t) = t + 1\) for \(0 \le t \le 3\). Which integral gives the total area swept as \(t\) varies?

🔹 A. \(\int_0^3 (2t)(t + 1) \, dt\)

🔹 B. \(\int_0^3 (2t) + (t + 1) \, dt\)

🔹 C. \(\int_0^3 \frac{2t}{t + 1} \, dt\)

🔹 D. \(\int_3^0 (2t)(t + 1) \, dt\)

💡 Difficulty: medium | ✅ Correct: A

Q3. A sequence of functions is defined by \(F_n(x) = \sum_{k=1}^{n} \frac{x^k}{k}\). Which integral represents the limit function as \(n \to \infty\) for \(0 \le x < 1\)?

🔹 A. \(\int_0^x \frac{1}{1 - t} \, dt\)

🔹 B. \(\int_0^x \frac{t}{1 - t} \, dt\)

🔹 C. \(\int_0^x \frac{t}{t} \, dt\)

🔹 D. \(\int_0^x \frac{1}{t} \, dt\)

💡 Difficulty: hard | ✅ Correct: A

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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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