📝 Integration By Substitution

📖 From Calculus • 6. Integration • 21 questions available

Practice MCQs for Integration By Substitution. 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. Which integral is most naturally solved by letting \(u = x^2\)?

🔹 A. \(\int 2x e^{x^2} \, dx\)

🔹 B. \(\int x \cos(x) \, dx\)

🔹 C. \(\int e^x \, dx\)

🔹 D. \(\int \frac{1}{x} \, dx\)

💡 Difficulty: easy | ✅ Correct: A

Q2. A dragster's velocity is given by \(v(t) = 4t^3 - 2t\) (meters per second). Using substitution, find the distance traveled from \(t = 0\) to \(t = 2\). Which integral correctly represents the distance?

🔹 A. \(\int_0^2 (12t^2 - 2) \, dt\)

🔹 B. \(\int_0^2 (12t^2 - 2t) \, dt\)

🔹 C. \(\int_0^2 (12t^2 - 2) \, dt\)

🔹 D. \(\int_0^2 (12t^2 - 2) \, dt\)

💡 Difficulty: medium | ✅ Correct: C

Q3. For the integral \(\int \frac{x^3}{\sqrt{1 + x^4}} \, dx\), which substitution is most effective?

🔹 A. \(u = 1 + x^4\)

🔹 B. \(u = x^2\)

🔹 C. \(u = x^4\)

🔹 D. \(u = \sqrt{1 + x^4}\)

💡 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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