4. Multiple Integrals

Triple Integrals — Quiz

Test your understanding of triple integrals with 5 practice questions.

Practice Questions

Question 1

Which of the following represents the general form of a triple integral in Cartesian coordinates for a function $f(x,y,z)$ over a region $E$?

Question 2

What is the volume of the region bounded by the planes $x=0$, $y=0$, $z=0$, and $x+y+z=1$?

Question 3

Which of the following sets of limits correctly represents the triple integral for the volume of the region inside the sphere $x^2 + y^2 + z^2 = 4$ in spherical coordinates?

Question 4

Consider the region bounded by $x=0$, $y=0$, and $z=4 - x^2 - y^2$. What is the triple integral setup to find the volume of this region in cylindrical coordinates?

Question 5

Find the mass of a solid bounded by the paraboloid $z = x^2 + y^2$ and the plane $z = 4$, if the density is $\delta(x,y,z) = z$. Which of the following integrals correctly represents the mass in cylindrical coordinates?