Question

find the formula for the Riemann sum obtained by dividing the interval [a,b] into n equal subintervals and using the right hand endpoint for each ck. Then take the limit of these sums as n tends to infinity to calculate the area under the curve over [a,b].
f(x)= 3x+2x^2 over the interval [0,2]

Answer 1

righthand is the same as f(b-i(b-a)/n) (b-a)/n

Answer 2

\[\lim_{n\to inf}\sum_{i=0}^{n-1}f(b-i\frac{(b-a)}{n}) \frac{(b-a)}{n}\]
\[\lim_{n\to inf}\sum_{i=0}^{n-1}f(2-i\frac{(2-0)}{n}) \frac{(2-0)}{n}\]
or since a = 0, it might be easy to do f(a+i...), for i=1 to n instead

Answer 3

\[\lim_{n\to inf}\sum_{i=1}^{n}f(i\frac{2}{n}) \frac{2}{n}\]