15-18-express-the-limit-as-a-definite-integral-on-the-given-interval-lim-_n-rightarrow-infty-sum_i-5

Question

$15-18=$ Express the limit as a definite integral on the given
interval.
$$\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{x_{i}^{*}}{\left(x_{i}^{*}\right)^{2}+4} \Delta x,[1,3]$$

Katelyn Chen · Accepted Answer

if, in the following women were asked to rewrite it as a definite edible. So start off with we have to use our sign for an integral just this funny looking symbol. And then we need to figure out the upper and lower limits which we know is based off of the range over here from our limit. So that will get us one as your lower and threes or upper. Next thing is to forget the function which we figure out from this part of limit that will get us X over X squared plus four. Lastly, we need to rewrite this as an integral form, which is DX. So this is our rewritten in general.

Katelyn Chen · Answer

we&#x27;re given the falling limit and we are asked to rewrite that stuff. So start off with we can use our definitely a girl symbol And then we know that we would you forget the upper limit alot elements. We know that space off for a given range. Do you know that are lower them is to honor upper this seven Then we have our function which we can derive from this part The limit which will get us five x cubed minus four X in the last part of limit is we need to write this. You know that for inter girls it is d X So this is our into cross.

Katelyn Chen · Answer

were given a following limit were asked to rewrite as a definite integral to start off with. We know that this is equal to the definite integral and so we need to figure upper, lower and lower limits. So we are given a ranges from 2 to 6. So you know that six is our upper and choose your lower lip. No, When you put a function well gets here, function is we&#x27;re here in this part of the equation. So we can basically just think of it s of XT I when you say it was X So then we have equal times entitled Explain one plus X squared and then the last part. We need to re represent this. Now remember, inter girls instead of this you will instead of this we have DX And so this is a religion as a definite integral

Amrita Bhasin · Answer

this question tells us to express the limit as a definite integral on the given interval. What we know is that we can use the formula. Ex Delta X is B minus eight over an ex advised A plus I. Delta X. Therefore, we can write this as the limit as an approaches infinity of our delta Eyes one and acts of I not shrug of one plus x of I squared times. Still, toe acts is equivalent to the integral from two to sex because they&#x27;ve given us the ace tune Be a sex natural. X Times natural log of one plus X squared D backs.

Katelyn Chen · Answer

even a phone limit your ass to rewrite as a definite integral to start off foot against a definite integral Simple. Now, when you figure out the upper lower limits mean which we know is based off of our give and redirect here. So, you know, our upper limit is two part in our lower limit is pie. Next new figure that equation inside. So we know it&#x27;s based off this section of the limit right here. And so basically think of and so excited. I just think of its X. So we have of co sign of X over X. Then we have to rewrite, um, Triangle X over here. So then we can we know that for into girls it is riveting as the X. So this is our definite into girl.

Stephen Hobbs · Answer

when rewriting a limit as an integral. We could always start with the interval that we&#x27;re interested in, and those were going to be the lower and upper limits to the integral. So the integral from 1 to 3 it&#x27;s how that&#x27;s red. And then by the time we get Thio except by stars, we can go ahead and replace all of this each of those exa by stars with exes. So that&#x27;ll be X divided by X squared plus four and then the Delta X There is the same thing or will change to a D X. And so the idea is, this is adding up an infinite number of rectangles whose heights are determined by this whole expression here and who&#x27;s with is a small amount of X or Delta X, and we transform that into this notation as an integral

Problem

$19-23$ . Use the form of the definition of the i…

Problem 18 Easy Difficulty

$15-18=$ Express the limit as a definite integral on the given
interval.
$$\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{x_{i}^{}}{\left(x_{i}^{}\right)^{2}+4} \Delta x,[1,3]$$

Answer

$\int_{1}^{3} \frac{x}{x^{2}+4} d x$

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$\int_{1}^{3} \frac{x}{x^{2}+4} d x$

Essential Calculus Early Transcendentals

Grace H.

Kayleah T.

Caleb E.

Joseph L.

Integration Review - Intro

Definite vs Indefinite

James StewartEssential Calculus Early Transcendentals

Grace H.

Kayleah T.

Caleb E.

Joseph L.

James Stewart

Essential Calculus Early Transcendentals