Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Riemann Sum question?
If the right and left Riemann sums give the same value, what does that mean in terms of the geometry of the graph?
1 Answer
- torquestompLv 41 decade agoFavorite Answer
It depends. Depending on how many sub-intervals you're using, it might just be a random coincidence and not mean anything.
However, consider the Riemann Sum of sin(x) on the interval [0, pi]
You can show algebraically that for any number of sub-intervals LHS = RHS. This is because sin(x) is symmetric around pi/2, the midpoint of the interval. You can prove that for any function f(x) symmetric around (a+b)/2, LHS[a,b] = RHS[a,b].
However, in general, showing that two Riemann-sum approximations are equal doesn't add up to any significance, because the Riemann Sum is just that: an approximation. What we really care about is the definite Integral, where the exact answer can be obtained.
