anonymous one year ago Write the integral that produces the same value as $\lim_{n \rightarrow \infty } \sum_{i=1}^{n}(3+i(5/n)^2)(5/n)$

1. anonymous

First, what do you think it would be?

2. anonymous

$\int\limits_{0}^{5}(3+5x)dx$

3. anonymous

I just dont understand what goes where

4. anonymous

@agentc0re

5. anonymous

Sorry the site went down for me, maybe you too?

6. anonymous

Yeah it did for me too

7. anonymous

Well lets remember that an integral is the sum between a and b where $\int\limits_{a}^{b} some\ equation\ here$

8. anonymous

okay yeah i got that. would a equal what i equals or something else?

9. anonymous

correct, in this case, a=1 and b=$\infty$

10. anonymous

Okay. Now what about the equation?

11. anonymous

well do you think it would be something different than what it currently is?

12. anonymous

if it helps, you can change n to be x so you have a dx at the end of the integral. but a dn would be fine too.

13. anonymous

no but for all the answers that are given to me they are all different $\int\limits_{8}^{3}(x^3)dx$ $\int\limits_{3}^{0}(x+3)^2dx$ $\int\limits_{5}^{0}(3+5x)dx$

14. anonymous

Ohh i read this wrong. i was thinking that i was imaginary. im dumb. I'm going to work this out on paper real quick and get back with you, okay?

15. anonymous

Okay thank you

16. anonymous

Im stumped as my calculus is proving to be a bit rusty. Here is what i do know though. http://www.wolframalpha.com/input/?i=lim+n-%3Einf+%28sum_%28i%3D1%29%5En++%283%2Bi%285%2Fn%29%5E2%29%285%2Fn%29%29+ So that limit = 15. Now you just need to compute your choices and see which one gives you an answer of 15.

17. anonymous

well none of them gave me 15

18. anonymous

Well damn. Im sorry. Try to ping one of the other helpers. I'm stumped on this one.

19. anonymous

Okay don't worry about it