How do I convert this into a definite integral?

hold on.. let me post it

Question

How do I convert this into a definite integral?

hold on.. let me post it

justjm · Answer

So I know that b-a=5 because delta x is 5/n, but I don't understand the f(xi*) part..

justjm · Answer

is $a$ 1? Then $b$ is 6. But I can't determine what f(x) is

justjm · Answer

$ \lim_{x \to \infty} \sum_{i=1}^{n}\frac{10i}{n}\left(\sqrt{1+\frac{5i}{n}}\right)\left(\frac{5}{n}\right) $

baileeisathey · Answer

what grade is this

baileeisathey · Answer

bc I'm going to cry when I have to learn thisXD

jhonyy9 · Answer

@justjm can you post the original text of this problem ?

so just bc. you wann calcule limit of an expression when x going to infinit and inside this expression you havent x

jhonyy9 · Answer

and there is a summ of this expression when i=1 till i=n

i think you need getting a resulted simplify form of this sum

jhonyy9 · Answer

and so i think you will can convert it in to a definite integral

justjm · Answer

I actually understand it now. Essentially the $ f(x^*_i) = f( \frac{5i}{n}) $ so I just had to solve it out. So the function is $ 2x \sqrt{1+x} $. I was just confused on how there was a 10i/n outside, but it was actually a part of the function. Thanks @jhonny9

jhonyy9 · Answer

np

with my pleasure - have a nice day

good luck