4. Multiple Integrals

Double Integrals In Polar Coordinates — Quiz

Test your understanding of double integrals in polar coordinates with 5 practice questions.

Practice Questions

Question 1

Convert the double integral $\iint_{R} (x^2 + y^2) \, dA$ over the region $R$ bounded by $x^2 + y^2 = 4$ into polar coordinates.

Question 2

Evaluate the integral $\int_{0}^{2\pi} \int_{0}^{3} r \, dr \, d\theta$.

Question 3

Which of the following integrals correctly represents the area of the region inside the circle $r = 2 \cos\theta$?

Question 4

Evaluate the double integral $\int_{0}^{\pi} \int_{0}^{1} r^3 \, dr \, d\theta$.

Question 5

Find the value of the integral $\int_{0}^{2\pi} \int_{0}^{1} (2r \sin\theta) \, r \, dr \, d\theta$.