Rienmann Sum??

Question

If f(x) = ln(x) - 1, 1 <= x <= 4, evaluate the Rienmann sum, taking sample points to be left endpoints. Answer should be correct to six decimal points.
oh and <= "means less than or equal to"...
10 points for the CORRECT answer!!
thank you!

Answer 1

You don't say how many points to use,so I am going to use 3. These are three intervals each of length 1: [1,2], [2,3], [3,4].

S = f(1)*1 + f(2)*1 +f(3)*1 = -1 -.306853 + .098612
= -1.208241

Answer 2

We partition the interval [1,4] into n subintervals, and we get the subintervals [x_i,x_(i+1)] for i = 0, 1, ... , n-1, where
x_i = 1 + 3/n. The Riemann sum is

Sum{f(x_i)*3/n} from 1 = 0 to n - 1, and f(x) = ln x - 1. You didn't tell us what value of n to use, so you take it from here.

Answer 3

-0.4548226 I did the integral because for 6 decimals accuracy its easier because you would need 1000+ intervals otherwise.

Answer 4

It's Riemann sum. Not rienmann. Now this is not hard. You're just finding the area of the partition. You did area in what 7th, 8th grade? You can do it.