# What is the difference benween numeric integration and riemann sums?

• Jan 18th 2009, 11:23 AM
cjosephson
What is the difference benween numeric integration and riemann sums?
I am a student in AP Calulus BC and I have been wondering this question for a while. I am doing the course online, and one lesson was called "Riemann Sums". The next lesson was "Numeric Integration".... and they were very similar. Why are they separated like this? Why wouldn't riemann sums just be included in the numeric lesson?

Are riemann sums a type of numeric integration? If not, what is the difference between riemann sums and numeric integration?
• Jan 18th 2009, 11:30 AM
Jester
Quote:

Originally Posted by cjosephson
I am a student in AP Calulus BC and I have been wondering this question for a while. I am doing the course online, and one lesson was called "Riemann Sums". The next lesson was "Numeric Integration".... and they were very similar. Why are they separated like this? Why wouldn't riemann sums just be included in the numeric lesson?

Are riemann sums a type of numeric integration? If not, what is the difference between riemann sums and numeric integration?

Riemann sums are a type of numerical integration but you'd need a lot of function evaluations (i.e. rectangles) to get a fairly accurate answer. However if you approximate the area under a curve, say with trapezoids (the trapezoid rule) or parts of parabola's (Simpson's rule), with the same number of function evaluations you can get a far more accurate answer or use few function evaluations to get an anwer accurate to a certain tolerence.
• Jan 18th 2009, 12:18 PM
cjosephson
OK, thats what I was hoping the answer was! Thanks