14. Divergence Theorem and Final Review

Triple Integral Formulation — Quiz

Test your understanding of triple integral formulation with 5 practice questions.

Practice Questions

Question 1

What is the value of $\iiint_E 1\,dV$ for the box $E=[0,2]\times[0,3]\times[0,4]$?

Question 2

Which iterated integral correctly represents $\iiint_E f(x,y,z)\,dV$ for the region $E$ given by $0\le z\le1$, $0\le y\le z$, and $0\le x\le y$?

Question 3

What does $\iiint_E 1\,dV$ represent for a solid region $E$?

Question 4

A solid $E$ has volume $6$ and constant density $\rho=5$. What mass is computed by $\iiint_E \rho\,dV$?

Question 5

Evaluate $\iiint_E x\,dV$ over the box $0\le x\le2$, $0\le y\le1$, $0\le z\le1$.