BetaCalculus Corner is in beta: things may change while we test, and payments aren't open yet.

© Calculus CornerGetting started Terms Privacy Contact

Chapter 16Line and Surface Integrals

0116.01Vector Fields
0216.02Line Integrals
0316.03Line Integrals of Vector Fields
0416.04The Fundamental Theorem for Line Integrals
0516.05Conservative Vector Fields
0616.06Green's Theorem
0716.07Area of Parametric Surfaces
0816.08Surface Integrals
0916.09Surface Integrals of Vector Fields
1016.10Stokes' Theorem
1116.11The Divergence Theorem
1216.12Applications of Line and Surface Integrals

Chapter 16 · Line and Surface Integrals

0116.01Vector Fields
0216.02Line Integrals
0316.03Line Integrals of Vector Fields
0416.04The Fundamental Theorem for Line Integrals
0516.05Conservative Vector Fields
0616.06Green's Theorem
0716.07Area of Parametric Surfaces
0816.08Surface Integrals
0916.09Surface Integrals of Vector Fields
1016.10Stokes' Theorem
1116.11The Divergence Theorem
1216.12Applications of Line and Surface Integrals

Topics / 16 Line and Surface Integrals

16.09

Surface Integrals of Vector Fields

The flux of a field through a surface: how much flows across it, counting the component along the normal.

About 15 minutes

You'll learn to

→Choose an orientation for a surface
→Compute flux ∬ F · dS with a parametrization
→Compute flux through graphs, spheres and cylinders

← 16.08 Surface Integrals 16.10 Stokes' Theorem →

Semester Pass

Unlock this lesson and every other topic

The full explanation, videos and 7 practice problems for this lesson are part of the Semester Pass: $49 once for 4 months of full access. No subscription, nothing renews.

Create a free account What's included

The first section of every chapter is free. Try 16.01 Vector Fields.