Integration or Riemann Sums: Which is More Effective for Numerical Integration?

[Apost8]

Is there ever a situation where it is more appropriate/advantageous to use Riemann summation as opposed to evaluating an integral, or is Riemann summation merely taught in order to help the student to understand what's going on?

 

[Beeza]

I always thought the Riemann sum was more fun to do!

 

[dontdisturbmycircles]

I would say that Riemann sums are taught primarily for grasping the concept of integration. It becomes impractical/impossible for complex functions and I can't think of a time when it would be easier.

 

[arildno]

Riemann sums are not "merely" taught to "understand what is going on".
They are taught because the PROOFS of Riemann integration depend on them, and as it happens, it is proofs that constitute the soul of maths, not nifty calculation techniques.

 

[dontdisturbmycircles]

Thats true.

 

[HallsofIvy]

Numerical integration techniques are based on Riemann sums.

Also, typically the way one sets up an integral in a particular application is typically based on the Riemann sum concept.