surface integrals

(1.7 hours to learn)


A surface integral is the integral of a function over a surface. Important cases include surface area and flux, where the function is the dot product of the surface normal with a vector field.


This concept has the prerequisites:


  • Know the definition of a surface integral in three dimensions.
  • Be able to integrate a function over a surface in three dimensions.
  • As a special case, be able to compute surface area.
  • Be able to compute the flux across a surface in three dimensions.
  • Derive the formula for a surface integral for a surface given as z = f(x, y).

Core resources (read/watch one of the following)


MIT Open Courseware: Multivariable Caclulus (2010)


Supplemental resources (the following are optional, but you may find them useful)


See also

-No Additional Notes-