← Back to 7. Applications of the Definite Integral In Geometry, Science, and Engineering

📝 Center Of Gravity Of Alamina

📖 From Calculus • 7. Applications of the Definite Integral In Geometry, Science, and Engineering • 22 questions available

Practice MCQs for Center Of Gravity Of Alamina. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-16

Easy Questions

Medium Questions

Hard Questions

📝 Sample Questions

Q1. For a thin lamina occupying the region bounded by \(y=x^2\) and \(y=4\) with uniform density, what is the x‑coordinate of its centroid?

🔹 A. \(\displaystyle \frac{1}{2}\int_{-2}^{2} x(4-x^2)\,dx\)

🔹 B. \(\displaystyle \frac{1}{A}\int_{-2}^{2} x(4-x^2)\,dx\)

🔹 C. \(\displaystyle \frac{1}{A}\int_{-2}^{2} (4-x^2)\,dx\)

🔹 D. \(\displaystyle \frac{1}{A}\int_{-2}^{2} x^2\,dx\)

💡 Difficulty: easy | ✅ Correct: B

Q2. A lamina occupies the region between \(y=x^3\) and \(y=0\) from \(x=0\) to \(x=1\). Its density is \(\rho=5\). Which expression correctly computes the x‑coordinate of the centroid?

🔹 A. \(\displaystyle \frac{1}{A}\int_{0}^{1} x\,(5x^3)\,dx\)

🔹 B. \displaystyle \frac{1}{A}\int_{0}^{1} 5x^3\,dx

🔹 C. \displaystyle \frac{1}{A}\int_{0}^{1} x^2\,dx

🔹 D. \displaystyle \frac{1}{A}\int_{0}^{1} x^4\,dx

💡 Difficulty: medium | ✅ Correct: A

Q3. A lamina has density \(\rho(x,y)=x^2+y^2\) over the unit square \([0,1]\times[0,1]\). What is the total mass?

🔹 A. \(\displaystyle \int_{0}^{1}\int_{0}^{1}(x^2+y^2)\,dy\,dx\)

🔹 B. \(\displaystyle \int_{0}^{1}\int_{0}^{1}(x+y)\,dy\,dx\)

🔹 C. \displaystyle \int_{0}^{1}\int_{0}^{1}xy\,dy\,dx

🔹 D. \displaystyle \int_{0}^{1}\int_{0}^{1}x^2y^2\,dy\,dx

💡 Difficulty: hard | ✅ Correct: A

⬆️ View all questions in the quiz below

🔗 Related Topics

📝 Approximating Roots 📝 Areas and Limits 📝 Continuity in Applications 📝 Continuity of Compositions 📝 Continuity of Inverse Functions

🚀 Start Quiz 📝 Practice Mode