1. 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.

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.

2. Yes, the subintervals are $\displaystyle {\Delta}x=\frac{\pi}{2n}$

Right endpoint method:

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

$\displaystyle f(x_{k})=\lim_{n\to {\infty}}\left[\sum_{k=1}^{n}\left(\frac{{\pi}k}{2n}cos(\frac{{\p i}k}{2n})\right)\frac{\pi}{2n}\right]$

3. 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.

4. Yes. That is the right end point method

5. Great, thanks ...

Originally Posted by galactus
Yes. That is the right end point method
Thanks again. This part is starting to make some sense now.