Question

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

Answer 1

First, what do you think it would be?

Answer 2

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

Answer 3

I just dont understand what goes where

Answer 4

@agentc0re

Answer 5

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

Answer 6

Yeah it did for me too

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

Okay. Now what about the equation?

Answer 11

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

Answer 12

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.

Answer 13

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

Answer 14

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?

Answer 15

Okay thank you

Answer 16

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.

Answer 17

well none of them gave me 15

Answer 18

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

Answer 19

Okay don't worry about it