Here we go again...

L

Lizzie

Full Member
Joined
Sep 8, 2005
Messages
317
The problem:
Express the limit as a definite integral on the given interval:
lim as n approaches infinity then there's a big E thingy with an n on top and i=1 on the bottom then x<sub>i</sub> [0, Pi] . . .

My problem:
I saw limits like this in my text, but as I've mentioned before, the text is infinitely confusing. My next few problems are quite similar to this one, so help on this one will help me understand the next few.

EDIT : I messed up the problem... after x<sub>i</sub> there is sin x<sub>i</sub>
 
OK, I've seriously read and reread the text and I do NOT get it!! *cries in frustration* BLEH! the next part of the problem is to evaluate
(there's this long line thing with 5 at the top and -1 at the bottom) (1+3x)dx
then, I have to evaluate (the big line thing again with a 2 at the top and a -2 at the bottom)(1- |x|)dx
Does that line thing with two numbers mean the interval?? If so then I am one smart cookie! If not then I'm beggin for your help here. :cry:
 
If you have "use Riemann sums and limits to integrate f(x) from x = a to x = b", how do you set this up? What does the result look like?

This question is asking you to go backwards. Starting from the Riemann sum and "letting n go to infinity", what was the integral that they were working on?

I can't tell what you're talking about in your second post, so I'm afraid I can't help there. Please either format what you're seeing using LaTeX, or else see about posting a scan.

Thank you.

Eliz.
 
In your second post is this what you are asked to evaluate?

\(\displaystyle \
\int_{ - 1}^5 {\left( {1 + 3x} \right)} {\rm }dx
\\)


You really should download TeXaide and use that to show your problems.
It's actually very easy to use. It would allow us to clearly see the problem you're
stuck on and allow us to help you faster.

What you are looking at is a definite integral which when evaluated gives you a number. The long s sign is called the integral sign and it means to integrate.

Make sure you understand the difference between a definite integral and an indefinite integral.

The numbers on the top and the bottom of the integral sign tell us it is a
definite integral. The bottom number is our lower limit of integration.
The top number is our upper limit of integration.


To evaluate a definite integral we do as follows,

Integrate as you normally would using indefinite integration,

we find the indefinite integral to be,

\(\displaystyle \
x + \frac{3}{2}x^2 + C
\\)

We can drop the C since it will always cancel out when
evaluating a definite integral. Evaluating our integral
at the given lower and upper limits we have,

\(\displaystyle \
\left[ {x + \frac{3}{2}x^2 } \right]_{ - 1}^5
\\)

To evaluate this we plug in 5 for the x's and -1 for the x's and subtract
the bottom limit from the top limit.

\(\displaystyle \
\left[ {5 + \frac{3}{2}(5)^2 } \right] - \left[ {( - 1) + \frac{3}{2}( - 1)^2 } \right]
\\)

Simplifying we find our answer to be 42. Which is of course the answer to
life, the universe, and everything. <g>

http://www.google.com/search?hl=en&...+life+the+universe+and+everything&btnG=Search
 
Thank you both very much. Opti, that is what I was talking about and I will definitely try to use that LaTex stuff in the future.
 
I actually UNDERSTAND the second one! Maybe then I can get the third one done, here's my steps.

The integral of this one is:

(x-|.5x<sup>2</sup>|), so then I plug in 2 and -2.

(2-|.5(2)<sup>2</sup>|)-(-2-|.5(-2)<sup>2</sup>|)

(2-2=0)-(-2-2=-4), 0+4=4,

Is that correct?
 
........................n
...................----------
....................\
......................\
.......lim............>............x<sub>i</sub> sinx<sub>i</sub> [0, Pi]
.n-> infinity...../
..................../
...................----------
........................i=1


Is that a little bit better??
 
Lizzie said:
Is that a little bit better?
Click to expand...
I can't make heads or tails of it. Sorry.

Please use the LaTeX. Thank you.

Eliz.
 
Is this what you mean Lizzie?:

\(\displaystyle \lim_{n\to\infty}\sum_{i=0}^nx_i\cdot\sin(x_i), x=[0,{\pi}]\)

That "big E thingy" is the capital Greek letter Sigma. It is used to represent sums.

If you want to know how I done the LaTex thing, click on the 'quote' icon in the

upper right hand corner of this post.
 
Use the "Forum Help" pull-down menu at the very top of the page.

Eliz.

P.S. To do spacing (if not using "Code" tags), change the color of your dots to "white". You can then indent, but the dots forcing the indentation will be nearly invisible. (If you go to a post where I've indented text, you can highlight from before the indentation to after, and you should see a line of white periods at the beginning of the indented line. I learned that trick from the master formatter, Soroban.)
 
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