Question

Hey guys looking for some help asap, medal of course, it involves rieman sums and calculus, I will post the question below. An explanation would be great, thanks

Answer 1

I remember my first integral. I'll do my best to explain it, but if I don't respond immediately it's because I'm in the next room making a delicious sandwich.

Answer 2

Express in terms of an integral and solve, do not use summation notation. \[Lim N \rightarrow \infty \sum_{i=1}^{n}(\sqrt{9+7i/n} \times (7/n)\]

Answer 3

Thanks, and yea it reads as the Limit as n approaches infinity of that function

Answer 4

I know it has to do with Delta X and Xi, but for some reason I cant see how to get it in the best form

Answer 5

What's your best guess or approach to solving this to begin with?

Answer 6

My best guess was to say that delta x must be 7/n and because xi= a+deltax and it looks as if a is 9, i said it would be \[\int\limits_{9}^{16}\sqrt{x}\]

Answer 7

im not sure if it is correct tho

Answer 8

Or would it be \[\int\limits_{0}^{7}\sqrt{9+x}\] ?

Answer 9

What about your 'dx' term on the end? I believe your second guess is almost right otherwise.

Answer 10

yea dx as well, but is it correct? if your not sure its okay but I need to know for a test soon

Answer 11

Yeah, I'll explain it right now, I just wanted to see how much you knew so I didn't have to waste my time overexplaining stuff you already know. =)

\[\lim_{n \rightarrow \infty} \sum_{i=1}^{n}\sqrt{9+\frac{ 7i }{ n}}*\frac{ 7 }{ n }\]
So as you recall, we're really just adding up the areas of rectangles with length and width.

That means the two things we're looking at here in an integral are going to be multiplied as well, which in the case appears to be straightforward, because it is.

So which is which? On is going to be how far we step every time we want to check the height of the rectangle and the other one will be the height itself. Since the height is checked at every step we take, it is dependent upon not only our step size but what the function is at that point. The step size will be uniform, for instance, we will only ever check it at every 4 points, or every 1/17th of a point or whatever.