anonymous
  • anonymous
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) = .
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
i have already figured out what a and b are but how do i find out what the function is?
experimentX
  • experimentX
ever heard a thing called latex? http://www.codecogs.com/latex/eqneditor.php
anonymous
  • anonymous
no i have never used this site.

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experimentX
  • experimentX
just type your equation here and post it here ... i can't make heads or tails out of you equation.
experimentX
  • experimentX
*there ... here
anonymous
  • anonymous
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
experimentX
  • experimentX
\[ \lim_{n \to \infty} \sum_{i=1}^{n} x_i \cos(x_i) \Delta x , \, [0,2\pi] \]
anonymous
  • anonymous
yeah thats it
experimentX
  • experimentX
just put that whole thing in \[ \text{\[} ... \text{\]} \]
anonymous
  • anonymous
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
experimentX
  • experimentX
and what are xi's?
anonymous
  • anonymous
im not sure. this is the entire problem
experimentX
  • experimentX
the problem is not complete. you are trying to convert Riemann sums into definite integral.
anonymous
  • anonymous
yeah we are not supposed to solve it he just wants us to identify what f(x) would be from this
experimentX
  • experimentX
the f(x) = x cos(x) to find the limit of integration, the given into is not enough to find a and b.
anonymous
  • anonymous
a=0 b = 2pi how did you find f(x)?
experimentX
  • experimentX
judging from the [0,2pi] given there, a=0, b=2pi
experimentX
  • experimentX
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.
anonymous
  • anonymous
Alright thanks
experimentX
  • experimentX
you need something like this. \[\lim_{n\to\infty} \sum_{k=1}^\infty \frac{ 2 \pi k}{n }\cdot \cos \left( \frac{ 2 \pi k}{n }\right) \cdot \frac{2\pi}{n} = \int_0^{2\pi} x \cos(x)dx \]

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