- #1
haackeDc
- 15
- 0
Homework Statement
Use the form of the definition of the integral to evaluate the following:
lim (n [itex]\rightarrow[/itex] ∞) [itex]\sum^{n}_{i=1}[/itex] x[itex]_{i}[/itex][itex]\cdot[/itex]ln(x[itex]_{i}[/itex][itex]^{2}[/itex] + 1)Δx on the interval [2, 6]
Homework Equations
x[itex]_{i}[/itex] = 2 + [itex]\frac{4}{n}[/itex]i
Δx = [itex]\frac{4}{n}[/itex]
Ʃ[itex]^{n}_{i=1}[/itex]i[itex]^{2}[/itex] = [itex]\frac{n(n+1)(2n+1)}{6}[/itex]
Ʃ[itex]^{n}_{i=1}[/itex]i = [itex]\frac{n(n+1)}{2}[/itex]
Ʃ[itex]^{n}_{i=1}[/itex]c = cn
The Attempt at a Solution
So far I've gotten it down to: lim (n [itex]\rightarrow[/itex] ∞) [itex]\frac{4}{n}[/itex][itex]\cdot[/itex] [itex]\sum^{n}_{i=1}[/itex] [(2+[itex]\frac{4}{n}[/itex]i)[itex]\cdot[/itex]ln([itex]\frac{16}{n^{2}}[/itex]i[itex]^{2}[/itex] + [itex]\frac{16}{n}[/itex]i + 5)]
but I am unsure how to distribute the sigma into the natural log, or how to get the i's out of the log... in short I can't think of a way to move forward!
I hope I wrote this clearly enough, can anyone assist me?
EDIT: Just to be clear, I am trying to put it in a form such that I can get rid of the sigma(Ʃ)
Last edited: