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 $\int_0^1 \int_0^{\sqrt{1-x^2}} f(x,y) \, dy \, dx$ into polar coordinates.

Question 2

Evaluate the double integral $\int_0^{2\pi} \int_0^2 r^2 \, r \, dr \, d\theta$.

Question 3

Find the region of integration in polar coordinates for the integral $\int_{-1}^1 \int_0^{\sqrt{1-x^2}} f(x,y) \, dy \, dx$.

Question 4

Evaluate the double integral $\int_0^{\pi} \int_0^3 r \, dr \, d\theta$.

Question 5

What is the correct expression for the double integral of $f(x,y) = x^2 + y^2$ over the unit disk $x^2 + y^2 \leq 1$ in polar coordinates?