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 a given density function $\rho(x,y)$ over a region $R$ in the plane?

Question 2

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

Question 3

If a region $R$ is bounded by $x=0$, $x=1$, $y=0$, and $y=2$, and the density function is $\rho(x,y)=3$, what is the total mass of the lamina?

Question 4

What is the average value of a function $f(x,y)$ over a region $R$ with area $A$?

Question 5

Find the moment about the $x$-axis for a lamina with density function $\rho(x,y)=2x$ over the region bounded by $x=0$, $x=1$, $y=0$, and $y=3$. What is the correct expression for this moment?