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📝 Area Between Two Curves

📖 From Calculus • 7. Applications of the Definite Integral In Geometry, Science, and Engineering • 21 questions available

Practice MCQs for Area Between Two Curves. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-16

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Q1. What is the integral expression for the area between \(y = x^{2}\) and \(y = x\) on the interval \([0,1]\)?

🔹 A. \( \displaystyle \int_{0}^{1}\!\bigl(x - x^{2}\bigr)\,dx\)

🔹 B. \( \displaystyle \int_{0}^{1}\!\bigl(x^{2} - x\bigr)\,dx\)

🔹 C. \( \displaystyle \int_{0}^{1}\!\bigl(x + x^{2}\bigr)\,dx\)

🔹 D. \( \displaystyle \int_{0}^{1}\!x^{2}\,dx\)

💡 Difficulty: easy | ✅ Correct: A

Q2. A region is bounded by \(y = x^{3}\) and \(y = x\) between their intersection points. Which integral gives its area?

🔹 A. \( \displaystyle \int_{0}^{1}\!(x - x^{3})\,dx\)

🔹 B. \( \displaystyle \int_{0}^{1}\!(x^{3} - x)\,dx\)

🔹 C. \( \displaystyle \int_{-1}^{0}\!(x^{3} - x)\,dx\)

🔹 D. \( \displaystyle \int_{-1}^{1}\!(x^{3} - x)\,dx\)

💡 Difficulty: medium | ✅ Correct: A

Q3. A bridge deck is modeled by the region between \(y = 4 - \frac{x^{2}}{4}\) and the line \(y = 2\) from the points of intersection. What is the area of this region?

🔹 A. \( \displaystyle \int_{-2\sqrt{2}}^{2\sqrt{2}}\!\bigl(4 - \tfrac{x^{2}}{4} - 2\bigr)\,dx\)

🔹 B. \( \displaystyle \int_{-2\sqrt{2}}^{2\sqrt{2}}\!\bigl(2 - 4 + \tfrac{x^{2}}{4}\bigr)\,dx\)

🔹 C. \( \displaystyle 2\int_{0}^{2\sqrt{2}}\!\bigl(4 - \tfrac{x^{2}}{4} - 2\bigr)\,dx\)

🔹 D. Both A and C give the same value

💡 Difficulty: hard | ✅ Correct: D

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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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