1. ## quick question about riemann sum

I would like to know if the integral of 16/(x^2) can be approximated using a Riemann sum. The integrals are from 0 to 2. I am asking this because at one of the boundaries, (0), f(0) is undefined (approaches infinity). However, i used n=4 and got an answer of 45.5556 as the Riemann sum. But shouldn't the area be infinite? I know Riemann sums don't give exact numbers and all, but if this is the case, can the Riemann sum be used when one of the boundaries is undefined?

thanks for any help as i am completely confused right now

2. You just can't do left Riemann sum (I guess you can and get infinity), but can still do the midpoint and right Riemann sum.

3. Originally Posted by Linnus
You just can't do left Riemann sum (I guess you can and get infinity), but can still do the midpoint and right Riemann sum.
great, thanks so much, so basically all i do is :

f(.5)(.5) + f(1)(.5) + f(1.5)(.5) + f(2)(.5) = 45.5556

4. Originally Posted by RandomChampion
great, thanks so much, so basically all i do is :

f(.5)(.5) + f(1)(.5) + f(1.5)(.5) + f(2)(.5) = 45.5556
A easier way would be .5 [f(.5)+f(1)+f(1.5)+f(2)], but yea, that would be how you do a right Riemann sum. Remember the answer you get will be nowhere near the correct answer.

5. Originally Posted by Linnus
A easier way would be .5 [f(.5)+f(1)+f(1.5)+f(2)], but yea, that would be how you do a right Riemann sum. Remember the answer you get will be nowhere near the correct answer.
yea i realize that, once again thanks a lot!

6. Yes this integral is undefined, consider that

$\displaystyle 16\int_0^2\frac{dx}{x^2}=16\lim_{\varphi\to{0}}\in t_{\varphi}^2\frac{dx}{x^2}$ Now if you evaluate this integral keeping the limit in mind you will find it diverges to infinity.

7. Originally Posted by Mathstud28
Yes this integral is undefined, consider that

$\displaystyle 16\int_0^2\frac{dx}{x^2}=16\lim_{\varphi\to{0}}\in t_{\varphi}^2\frac{dx}{x^2}$ Now if you evaluate this integral keeping the limit in mind you will find it diverges to infinity.
wait so does that mean i can't use a riemann sum on it?

8. Originally Posted by RandomChampion
wait so does that mean i can't use a riemann sum on it?
You can...but it's basically pointless since the answer is infinity. The right and midpoint Riemann will not give you a correct answer. It wouldn't even be really consider an estimate of the integral, which is one of the purpose of the Riemann sum.

9. Originally Posted by Linnus
You can...but it's basically pointless since the answer is infinity. The right and midpoint Riemann will not give you a correct answer. It wouldn't even be really consider an estimate of the integral, which is one of the purpose of the Riemann sum.
ok, sorry for being so confused. so me using the right riemann will not be incorrect, no matter how off the resulting estimate is?

10. Originally Posted by RandomChampion
ok, sorry for being so confused. so me using the right riemann will not be incorrect, no matter how off the resulting estimate is?
It depends on what the question is asking you to do. If it explicitly state "estimate the integral using the right Riemann sum with n=4 on the interval [0,2]" there isn't really much you can do.

11. Originally Posted by Linnus
It depends on what the question is asking you to do. If it explicitly state "estimate the integral using the right Riemann sum with n=4 on the interval [0,2]" there isn't really much you can do.
ok heres the exact question:

Approximate the integral of 16/(x^2) dx using a Riemann sum with n=4, n=8

so i gues there are three possible answers for each n value?

12. Originally Posted by RandomChampion
ok heres the exact question:

Approximate the integral of 16/(x^2) dx using a Riemann sum with n=4, n=8

so i gues there are three possible answers for each n value?
Yes, there are 3 possible answers for each n value.

13. Originally Posted by Linnus
Yes, there are 3 possible answers for each n value.

ok great, thanks a lot for all the help!