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Limits & Riemman Sum

  • #1
169
0

Homework Statement


Question regarding #16

III-16.jpg



Homework Equations



Riemman Sum

The Attempt at a Solution



I know that the limit of the Riemman Sum is basically the integral. However, I do not know where to go from there. Do I need to use the Summation formulas? Thanks
 

Answers and Replies

  • #2
rbj
2,226
7
can you write down the expression for a Riemann integral. something like:

[tex] \int_a^b f(x) dx = \lim_{N \to \infty} \sum_{n=1}^N ??? [/tex]

what goes in the question marks?

also, even though Riemann doesn't, assume things in the ??? are equally spaced. that's usually good enough.
 
Last edited:
  • #3
169
0
can you write down the expression for a Riemann integral. something like:

[tex] \int_a^b f(x) dx = \lim_{N \to \infty} \sum_{n=1}^N ??? [/tex]

what goes in the question marks?

also, even though Riemann doesn't, assume things in the ??? are equally spaced. that's usually good enough.
Well, here's what I have so far:

[tex] \int_a^b f(x) dx = \lim_{N \to \infty} \sum_{n=1}^N (\frac{1}{N}\sin(\frac{\pi i}{N})[/tex]
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,792
920
So what part of that sum is dx and what part is f(x)? After you know f(x), what is its integral?
 

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