Question

The following limit
limn→∞∑i=1nxicos(xi)Δx,[0,2π]


is equal to the definite integral ∫baf(x)dx where a = , b = ,

and f(x) = .

Answer 1

i have already figured out what a and b are but how do i find out what the function is?

Answer 2

ever heard a thing called latex?
http://www.codecogs.com/latex/eqneditor.php

Answer 3

no i have never used this site.

Answer 4

just type your equation here and post it here ... i can't make heads or tails out of you equation.

Answer 5

*there ... here

Answer 6

i dont know how to type it out.

\lim_{n \to \infty} \sum_{i=1}^{n} x_i \cos(x_i) \Delta x , \, [0,2\pi] this is the math code and if you put it into latex it will translate

Answer 7

\[ \lim_{n \to \infty} \sum_{i=1}^{n} x_i \cos(x_i) \Delta x , \, [0,2\pi] \]

Answer 8

yeah thats it

Answer 9

just put that whole thing in
\[ \text{\[} ... \text{\]} \]

Answer 10

alright so how do i find the f(x) of this? I have looked at things online, but they are not making any sense to me

Answer 11

and what are xi's?

Answer 12

im not sure. this is the entire problem

Answer 13

the problem is not complete. you are trying to convert Riemann sums into definite integral.

Answer 14

yeah we are not supposed to solve it he just wants us to identify what f(x) would be from this

Answer 15

the f(x) = x cos(x)
to find the limit of integration, the given into is not enough to find a and b.

Answer 16

a=0 b = 2pi
how did you find f(x)?

Answer 17

judging from the [0,2pi] given there, a=0, b=2pi

Answer 18

as i told you the given info is not strong enough to find f(x) and the limits a and b. you should define your xi's and delta x first.

Answer 19

Alright thanks

Answer 20

you need something like this.
\[\lim_{n\to\infty} \sum_{k=1}^\infty \frac{ 2 \pi k}{n }\cdot \cos \left( \frac{ 2 \pi k}{n }\right) \cdot \frac{2\pi}{n} = \int_0^{2\pi} x \cos(x)dx \]