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📝 Reversing The Roles Of X And Y

📖 From Calculus • 7. Applications of the Definite Integral In Geometry, Science, and Engineering • 20 questions available

Practice MCQs for Reversing The Roles Of X And Y. 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. For the region bounded by \(y = x^2\) and \(y = 4\), what are the limits of integration when the integral is written in terms of \(y\) instead of \(x\)?

🔹 A. 0 to 4

🔹 B. -2 to 2

🔹 C. 0 to 2

🔹 D. -4 to 4

💡 Difficulty: easy | ✅ Correct: A

Q2. A solid has cross‑sections perpendicular to the \(y\)-axis that are squares. The base region is bounded by \(x = y^2\) and \(x = 2y + 3\). Which integral yields the volume?

🔹 A. \(\displaystyle\int_{-1}^{3}\big[(2y+3) - y^2\big]^2\,dy\)

🔹 B. \(\displaystyle\int_{-1}^{3}\big[(2y+3) - y^2\big]\,dy\)

🔹 C. \(\displaystyle\int_{-1}^{3}\big[(2y+3) + y^2\big]^2\,dy\)

🔹 D. \(\displaystyle\int_{-1}^{3}\big[(2y+3) + y^2\big]\,dy\)

💡 Difficulty: medium | ✅ Correct: A

Q3. A curve defined by \(y = \frac{x}{1+x^{2}}\) intersects the line \(y = \frac{1}{2}\). After swapping variables, which integral computes the area between them?

🔹 A. \(\displaystyle\int_{0}^{1}\left(\frac{1}{2} - \frac{x}{1+x^{2}}\right)dx\)

🔹 B. \displaystyle\int_{0}^{1}\left(\frac{x}{1+x^{2}} - \frac{1}{2}\right)dx\)

🔹 C. \displaystyle\int_{0}^{\frac{1}{2}}\left(\frac{1}{2} - \frac{y}{1-y^{2}}\right)dy\)

🔹 D. \displaystyle\int_{0}^{\frac{1}{2}}\left(\frac{1}{2} - \frac{y}{1-y^{2}}\right)dx\)

💡 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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