Writing a Riemann Sum w/out Sumation signs

[REPharaoh]

Homework Statement

In this problem you will calculate ∫0,4 ( [(x^2)/4] − 7) dx by using the definition

∫a,b f(x) dx = lim (n → ∞) [(n ∑ i=1) (f(xi) ∆x)]

The summation inside the brackets is Rn which is the Riemann sum where the sample points are chosen to be the right-hand endpoints of each sub-interval.

Calculate Rn for f(x) = (x^2)/4] − 7 on the interval [0, 4] and write your answer as a function of n without any summation signs.

Homework Equations

I guess the relevant equations are n(n+1)(2n_1)/6 and (n(n+1))/2

The Attempt at a Solution

I followed several guides on line and my solution comes up with the integral, however it is not correct when I submit it.

(32/(4n^3))((n(n+1)(2n+1))/6)-(64/(4n^3))(n(n+1)/2)+(32/(4n^3)(n))-((14/n)(n))


NOTE:

See attached files to make more sense of the problem.

 

[lippyka]

The solution I should get is (32/(4n^3))((n(n+1)(2n+1))/6)-(64/(4n^3))(n(n+1)/2)+(32/(4n^3)(n))-((14/n)(n))+(56/n)