5. Vector Calculus

Divergence Theorem — Quiz

Test your understanding of divergence theorem with 5 practice questions.

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Practice Questions

Question 1

Which of the following best describes the Divergence Theorem?

Question 2

Consider the vector field $\mathbf{F}(x,y,z) = (x^2, y^2, z^2)$. What is the divergence of $\mathbf{F}$?

Question 3

Use the Divergence Theorem to find the flux of the vector field $\mathbf{F}(x,y,z) = (2x, 3y, 4z)$ through the surface of the cube bounded by $x=0$, $x=1$, $y=0$, $y=1$, $z=0$, and $z=1$.

Question 4

Which of the following conditions must hold for the Divergence Theorem to be applied to a vector field $\mathbf{F}$ over a region $V$?

Question 5

Let $\mathbf{F}(x,y,z) = (y, z, x)$. Compute the flux of $\mathbf{F}$ through the surface of the unit sphere $x^2 + y^2 + z^2 = 1$ using the Divergence Theorem.