Surface Integral Quizzes, Questions & Answers

Top Trending Surface Integral Quizzes

Flux Integrals of Vector Fields: Definition, Setup & Physical Meaning

This quiz focuses on core techniques of surface integration, including computing scalar surface integrals, evaluating flux using normal vectors, applying parameterizations, and using surface area elements for graphs and implicit...

Questions: 15 | Attempts: 13 | Last updated: Feb 6, 2026

Sample Question 1
Which of the following represents the correct formula for the surface area element dS for a surface defined explicitly by z = g(x, y)?

DS = (1 + (dg/dx) + (dg/dy)) dA

DS = √(1 + (dg/dx)² + (dg/dy)²) dA

DS = √((dg/dx)² + (dg/dy)²) dA

DS = ((dg/dx)² + (dg/dy)²) dA

Sample Question 2
We wish to evaluate the surface integral of the scalar function f(x, y, z) = z over the part of the plane z = 2 - x - y that lies in the first octant. Which double integral correctly sets up this problem?

Integral over D of (2 - x - y) dx dy

Integral over D of (2 - x - y) * √(3) dx dy

Integral over D of z * √(1 + x² + y²) dx dy

Integral over D of (2 - x - y) * 3 dx dy

Advanced Surface & Flux Integrals: Symmetry, Projections & Mixed Applications

This quiz focuses on evaluating scalar and vector surface integrals, including surface areas, flux through oriented surfaces, and applications of gradients and the Divergence Theorem. You will work with surfaces given...

Questions: 14 | Attempts: 11 | Last updated: Feb 6, 2026

Sample Question 1
Evaluate ∬ₛ 1 dS for the surface S given by z = x + y, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 - x.

√3

√3 / 2

√3 * 1/2

2√3

Sample Question 2
Compute the surface area ∬ₛ dS where S is the part of the plane x + y + z = 1 in the first octant.

√2/2

√3/2

1/2

√3

Recent Surface Integral Quizzes

Surface Integrals, Heat Flow & Divergence Theorem Intuition

Questions: 15 | Attempts: 10 | Last updated: Dec 17, 2025

Sample Question
What does a flux integral physically represent?

The total mass of a surface

The net flow of a vector field through a surface

The average value of a function on a surface

The surface area of the region

Surface Integrals of Scalar Fields: Surface Area & Basic Applications

Questions: 15 | Attempts: 10 | Last updated: Feb 6, 2026

Sample Question
What is the surface integral of the scalar function f(x,y,z)=2 over the surface S, which is the unit disk in the xy-plane (z=0)?

0

π

2π

4π