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PrevlousProblem ListNextpoint) Find the length of the curve defined by61*/2 +11from x2 t0The length isPreview My AnswersSubmit AnswersYou have attempted this proble...

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PrevlousProblem ListNextpoint) Find the length of the curve defined by61*/2 +11from x2 t0The length isPreview My AnswersSubmit AnswersYou have attempted this problem tlmes Your overall recorded score is 0% You have unlimited attempts remaining:

Prevlous Problem List Next point) Find the length of the curve defined by 61*/2 +11 from x 2 t0 The length is Preview My Answers Submit Answers You have attempted this problem tlmes Your overall recorded score is 0% You have unlimited attempts remaining:



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Find the are length function for the graph of $f(x)=2 x^{3 / 2}$ using (0,0) as the starting point. What is the length of the curve from (0,0) to (1,2)$?$

This problem with your reflection at first to find a journalist sparkling function. And then we're us. Tiu belay that our plane between 00212 So we don't have the general person doing more simple are like opening function is for it to be Oh, spirit of one plus df dx spray sometimes the eggs. So we needed their help dysfunction less persuading barrett or dysfunction. You've been a you find there didn t f he has to be. To be or to exit will help. So we find that there were two then to be free exit of one help less like that in Yeah s for arranging the skirted off woman waas The FDA spreads originally nine. Thanks. The eggs are in general home recon work. This one s art like has a bunch of eggs to be good to your duty towards your ex skirted woman plus 90 the teeth. So this is the general for Down. Let's find the Ark Ling. Between these two points, so s will be s exchanges from 01 This will be one plus x. You do? Yes. That will be going to then entire everything for its interment is on false nine eggs. You were too divided by feeling to terms. Well, Mary, let's fly be given while using, um, if you do so we find this to be your 27. Well, actually, let's rewrite this first. Now let's put one in. Unless like like Syria was. Some warn. So you find the answer to be there to over 27 10 to the poverty to over three months one. And that is because two or 27 10 screwed up 10 minus one.

Miss Programs First week, right. The privatization of the straight line will key rt close to 80 process peed in the Seiki Prosky. And this post that a zero. Because I want you in there one because to five points to, According to this information, we know that a close before seacoast one see coastal minus for the G force to to just called you on this parliament into this permit validation that gives us a system of equations by Soviet bestest on the question. We have this condition. So are key because Teoh for Keith Cross once in the minus 40 class, too. And the Oculus off this curve will be STD because they will be integral from zero to t fruit off. Ex prime square class life runs where you and me in this case on this is X, and this is why. So we have, um fourth time's wrote off to pee, which gives us P close to 1/4 times route off two times s so you can use this accidents to purple tries the curve. So are its equals. Two. Um, it's over the top to class one minus days over. Route off to for us to where is this between? A zero to some. Um, this upper bound for their for the domain off is because we know that's the starting point is 12 and the ending point is five my AR minus two. So the total in off this three. Time your peep fruit off four square plus foursquare. So is this picture zero in the fourth hands route off to.

Okay, so we know that the length of a curve, um f of X over an interval A B is well, is given by the integral from A to B of the square root of one plus the delimited here f prime of X squared the X. So here we have that a is equal 20 and we have that be is equal to eight. We have that A function f of X is equal to four minus X to the two thirds to the three halves. Okay, um, so then we go ahead and we need to find, well, f prime of X, right. And then schedule f prime of axe is gonna be equal to negative the square root of four minus acts to the two thirds, uh, over X to the one there. Okay, so now, well, I mean, the curve here is given by the integral from A to B. So the integral from 0 to 8 of the square reit off one plus the derivative square. So one plus a negative four minus acts to the two thirds all over X to the one third, and then we square that. And then, of course, we have a DX. Okay. Well, um, this move more scared than it really is. So well, this is gonna be equal to the integral from, um, 08 of one plus four minutes extra two thirds over X to the, um, two thirds, which is equal. Chew. That s it becomes too pans the integral from 0 to 8 of just X to the negative one third the X, which is equal to two times three X to the to thirds over two. And they re evaluate from 0 to 8 since just equal to three times eight to the two thirds. Okay, Well, um, 8 to 2 through this. That's just a cube root of eight, which is two. And then we square it. So the eighth of the two thirds que put of 82 squared is four justice three times for which is equal. So the length of the plane curve in the given Integral is traum units

We must find the length of this curve, Y equals two thirds times the quantity X squared plus one, all to the three halves from X equals 12 X equals two. And so we will do this using our handy length of a curve um formula here. So first thing we have to do is find this dy dx. So let's compute the derivative of our function. So first we will bring down the power so we get a 3/2ves subtract one from the power on her. And then we have to use the chain rule. So We find the multiply by the derivative of the inside which is two X. And so here is our dy dx. In fact, these fractions will cancel. So it's a lot neater. Okay now we can compute are integral using this formula once again. So we will take the integral From 1 to 2, The square root of one us. So if we square this entire quantity we can we can distribute the square. Yeah, we write it out down here. Few idea, X squared equals. So we can distribute the square to these between the products. So we'll get x squared plus one to the one, 1/2 times two is 1 times for X squared. So let's just write that in right here. In fact, I'm even going to distribute this four X squared. So we'll get four X to the floor plus for X squared. Okay, D X. And so now this inside part can actually be factored. So if I like another section here, so if I had the plus one, you can notice that this can actually factored as two X squared plus one square. And you can see two x squared squared is forks to the floor and then two times two X squared plus times one is four X squared and so on. So the square root will cancel this square. So we're left with the integral from 1 to 2 of two x squared, yes plus one D X. And so now we can just evaluate this integral. So we use power rule 2/3 extra third plus X, worrying for 1 to 2. And so if we plug these in 2-38 Times two is 16 over three plus two. So this is the expression evaluated to minus if I were at one, which is simply one plus two thirds times one. So this will just be 5/3. And so you can simplify this down 22/3 minus five thirds, gives you 17 thirds.


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