Consider the function f(x) = (x^2)/3 + 2.?

Question

In this problem calculate the integral from 0 to 2 of f(x) =((x^2)/3 + 2 )dx by using the definition int of a to b of f(x) dx = lim of n to infty Sn {i=1}^{n} f(x_i)*Delta x
The summation inside the brackets is R_n which is the Riemann sum where the sample points are chosen to be the right-hand endpoints of each sub-interval.

Calculate R_n for f(x) = (x^2)/3 + 2 on the interval [0, 2] and write your answer as a function of n without any summation signs

R_n = ?
lim_{n to infty} R_n = ?

Answer 1

You are not specific enough ...you want a regular partition where each delta x = [b-a] / n.....R_n = [8n(n+1)(2n+1)] / 3 [n^3] 6 + [4n] / n........16/18 + 4