4. Multiple Integrals

Applications Of Multiple Integrals — Quiz

Test your understanding of applications of multiple integrals with 5 practice questions.

Practice Questions

Question 1

What is the formula for the mass of a lamina with density function $\rho(x,y)$ over a region $R$ in the $xy$-plane?

Question 2

Which of the following represents the formula for the moment about the $x$-axis for a lamina with density function $\rho(x,y)$ over region $R$?

Question 3

How do you find the average value of a function $f(x,y)$ over a region $R$?

Question 4

What is the formula for the $x$-coordinate of the center of mass of a lamina with density function $\rho(x,y)$ over region $R$?

Question 5

A lamina occupies the region $R$ defined by $0 \leq x \leq 1$ and $0 \leq y \leq 2$. The density function is $\rho(x,y)=3$. What is the mass of the lamina?