Question

Hello
On problem 3B-5 how can you know that the expression is a Right Reimann sum? Why isn't it a Left Reimann sum?

Answer 1

Here is a "picture"


It is natural to assume we start at sin(0) and let sin(b/n) (the first "y" value in the expression) represent the right-side of a rectangle of height sin(b/n) and width b/n

It is true we could assume that the first rectangle has its *left* side at sin(b/n), and integrate starting at x=b/n... making it a left Riemann sum... in the limit as we let n approach infinity we will get the same answer as assuming a right Riemann sum. However, to me it seems more natural to start at x=0 than at x= b/n, and that is what the answerer was also thinking.