📝 Other Types Of Regions

📖 From Calculus • 7. Applications of the Definite Integral In Geometry, Science, and Engineering • 23 questions available

Practice MCQs for Other Types Of Regions. 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

Q1. What does the term \( \Delta x_k \) represent in a Riemann sum?

🔹 A. Width of the k‑th subinterval

🔹 B. Height of the k‑th rectangle

🔹 C. Midpoint of the interval

🔹 D. Total width of all subintervals

💡 Difficulty: easy | ✅ Correct: A

Q2. Find the area between \( y = x^2 \) and \( y = 2x \) from \( x = 0 \) to \( x = 2 \).

🔹 A. \( \displaystyle \int_0^2 (2x - x^2)\,dx \)

🔹 B. \( \displaystyle \int_0^2 (x^2 - 2x)\,dx \)

🔹 C. \( \displaystyle \int_0^2 (2x + x^2)\,dx \)

🔹 D. \( \displaystyle \int_0^2 (2x)\,dx \)

💡 Difficulty: medium | ✅ Correct: A

Q3. A conical tank with height 6 m and base radius 3 m is full of water. How much work is required to pump all water to the top?

🔹 A. \( \displaystyle \rho g\int_0^6 \pi\left(\frac{r}{h}y\right)^2 (6-y)\,dy \)

🔹 B. \( \displaystyle \rho g\int_0^6 \pi\left(\frac{3}{6}y\right)^2 (6-y)\,dy \)

🔹 C. \( \displaystyle \rho g\int_0^6 \pi\left(\frac{3}{6}y\right)^2 y\,dy \)

🔹 D. \( \displaystyle \rho g\int_0^6 \pi\left(\frac{3}{6}y\right)^2 (6+y)\,dy \)

💡 Difficulty: hard | ✅ Correct: B

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