Write the integral that produces the same value as \[\lim_{n \rightarrow \infty } \sum_{i=1}^{n}(3+i(5/n)^2)(5/n)\]

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- anonymous

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- anonymous

First, what do you think it would be?

- anonymous

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

- anonymous

I just dont understand what goes where

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## More answers

- anonymous

- anonymous

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

- anonymous

Yeah it did for me too

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

Okay. Now what about the equation?

- anonymous

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

- 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.

- anonymous

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

- 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?

- anonymous

Okay thank you

- 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.

- anonymous

well none of them gave me 15

- anonymous

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

- anonymous

Okay don't worry about it

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