Question about Evaluating Integrals using Limits and Sigmas

• January 12th 2010, 06:31 PM
ckoeber
Question about Evaluating Integrals using Limits and Sigmas
OK, I hope this makes sense.

So I am taking my second class in calculus but there has been a three year lapse in the time I have taken the first class so I am a little rusty.

I am trying to create an expression for the area under the curve using limits.

Specifically, the question asks:

Use Definition 2 to find an expression for the area under the graph of f as a limit. Do not evaluate the limit.

Based on that I have garnered the following:

However, I am lost as to how to proceed. Any help that can explain this step by step would be greatly appreciated.
Thank you for your time.
• January 12th 2010, 06:56 PM
galactus
Yes, the subintervals are ${\Delta}x=\frac{\pi}{2n}$

Right endpoint method:

$x_{k}=\frac{{\pi}k}{2n}$

$f(x_{k})=\lim_{n\to {\infty}}\left[\sum_{k=1}^{n}\left(\frac{{\pi}k}{2n}cos(\frac{{\p i}k}{2n})\right)\frac{\pi}{2n}\right]$
• January 12th 2010, 07:19 PM
ckoeber
Thanks so much for the speedy response!

I do have a question. I noted that you used k to denote the part that changes in the sigma notation. So, you multiplied delta x by that variable?

And after that you substitued the resultant product into the original equation?

Thanks again.
• January 13th 2010, 04:17 AM
galactus
Yes. That is the right end point method
• January 13th 2010, 09:13 AM
ckoeber
Great, thanks ...
Quote:

Originally Posted by galactus
Yes. That is the right end point method

Thanks again. This part is starting to make some sense now.